├── .github └── workflows │ └── main.yml ├── .gitignore ├── README.md ├── final-version.pdf ├── meetings.md ├── questions ├── morse-inequalities-solution │ └── master.tex ├── morse-inequalities │ └── master.tex └── proof-cancellation │ ├── figures │ ├── setup.pdf │ ├── setup.pdf_tex │ └── setup.svg │ └── master.tex └── thesis ├── bibliography.bib ├── chap-outlook.tex ├── chap0.tex ├── chap1.tex ├── chap2.tex ├── chap3.tex ├── chap4.tex ├── chap5.tex ├── conclusion.tex ├── copyright.tex ├── figures ├── .svg ├── a-is-a-chain-map.pdf ├── a-is-a-chain-map.pdf_tex ├── a-is-a-chain-map.svg ├── a-is-left-inverse-to-d.pdf ├── a-is-left-inverse-to-d.pdf_tex ├── a-is-left-inverse-to-d.svg ├── abundance-of-morse-functions-parametrization-of-the-normal-bundle.pdf ├── abundance-of-morse-functions-parametrization-of-the-normal-bundle.pdf_tex ├── abundance-of-morse-functions-parametrization-of-the-normal-bundle.svg ├── addition-of-columns-geometrically.pdf ├── addition-of-columns-geometrically.pdf_tex ├── addition-of-columns-geometrically.svg ├── alteration-of-pseudogradient-vector-field.pdf ├── alteration-of-pseudogradient-vector-field.pdf_tex ├── alteration-of-pseudogradient-vector-field.svg ├── alteration-of-vector-field.pdf ├── alteration-of-vector-field.pdf_tex ├── alteration-of-vector-field.svg ├── any-closed-manifold-admits-a-handlebody-decomposition.pdf ├── any-closed-manifold-admits-a-handlebody-decomposition.pdf_tex ├── any-closed-manifold-admits-a-handlebody-decomposition.svg ├── approximate-morse-functions.pdf ├── approximate-morse-functions.pdf_tex ├── approximate-morse-functions.svg ├── assertion-1.pdf ├── assertion-1.pdf_tex ├── assertion-1.svg ├── assertion-4.pdf ├── assertion-4.pdf_tex ├── assertion-4.svg ├── assertion-5.pdf ├── assertion-5.pdf_tex ├── assertion-5.svg ├── bigger-figure.pdf ├── bigger-figure.pdf_tex ├── bigger-figure.svg ├── canellation-of-critical-points-situation.pdf ├── canellation-of-critical-points-situation.pdf_tex ├── canellation-of-critical-points-situation.svg ├── chain-homotopy-between-d-na-a-and-id.pdf ├── chain-homotopy-between-d-na-a-and-id.pdf_tex ├── chain-homotopy-between-d-na-a-and-id.svg ├── changing-one-handles-in-three-handles.pdf ├── changing-one-handles-in-three-handles.pdf_tex ├── changing-one-handles-in-three-handles.svg ├── codimensions-transverse.pdf ├── codimensions-transverse.pdf_tex ├── codimensions-transverse.svg ├── compactification-of-unstable-manifolds.pdf ├── compactification-of-unstable-manifolds.pdf_tex ├── compactification-of-unstable-manifolds.svg ├── connected-sum-homotopy-spheres.pdf ├── connected-sum-homotopy-spheres.pdf_tex ├── connected-sum-homotopy-spheres.svg ├── d-is-a-chain-map.pdf ├── d-is-a-chain-map.pdf_tex ├── d-is-a-chain-map.svg ├── d-na-a-is-not-identity.pdf ├── d-na-a-is-not-identity.pdf_tex ├── d-na-a-is-not-identity.svg ├── definition-boundary-singular-homology.pdf ├── definition-boundary-singular-homology.pdf_tex ├── definition-boundary-singular-homology.svg ├── definition-homotopy-groups.pdf ├── definition-homotopy-groups.pdf_tex ├── definition-homotopy-groups.svg ├── definition-relative-homology.pdf ├── definition-relative-homology.pdf_tex ├── definition-relative-homology.svg ├── definition-symplex.pdf ├── definition-symplex.pdf_tex ├── definition-symplex.svg ├── example-cancelling-handles-in-three-dimensions.pdf ├── example-cancelling-handles-in-three-dimensions.pdf_tex ├── example-cancelling-handles-in-three-dimensions.svg ├── example-when-fp-is-not-a-morse-function.pdf ├── example-when-fp-is-not-a-morse-function.pdf_tex ├── example-when-fp-is-not-a-morse-function.svg ├── examples-of-cobordisms.pdf ├── examples-of-cobordisms.pdf_tex ├── examples-of-cobordisms.svg ├── examples-of-morse-functions.pdf ├── examples-of-morse-functions.pdf_tex ├── examples-of-morse-functions.svg ├── existence-of-morse-functions-normal-bundle-map.pdf ├── existence-of-morse-functions-normal-bundle-map.pdf_tex ├── existence-of-morse-functions-normal-bundle-map.svg ├── finding-holes-using-singular-homology.pdf ├── finding-holes-using-singular-homology.pdf_tex ├── finding-holes-using-singular-homology.svg ├── fundamental-group-operation.pdf ├── fundamental-group-operation.pdf_tex ├── fundamental-group-operation.svg ├── genus-four-heegaard-splitting-of-s3.pdf ├── genus-four-heegaard-splitting-of-s3.pdf_tex ├── genus-four-heegaard-splitting-of-s3.svg ├── handle-1-0.pdf ├── handle-1-0.pdf_tex ├── handle-1-0.svg ├── handle-1-1.pdf ├── handle-1-1.pdf_tex ├── handle-1-1.svg ├── handle-2-0.pdf ├── handle-2-0.pdf_tex ├── handle-2-0.svg ├── handle-2-1.pdf ├── handle-2-1.pdf_tex ├── handle-2-1.svg ├── handle-2-2.pdf ├── handle-2-2.pdf_tex ├── handle-2-2.svg ├── handle-3-0.pdf ├── handle-3-0.pdf_tex ├── handle-3-0.svg ├── handle-3-1.pdf ├── handle-3-1.pdf_tex ├── handle-3-1.svg ├── handle-3-2.pdf ├── handle-3-2.pdf_tex ├── handle-3-2.svg ├── handle-3-3.pdf ├── handle-3-3.pdf_tex ├── handle-3-3.svg ├── handle-diffeo-homeo-homotopy-equivalent.pdf ├── handle-diffeo-homeo-homotopy-equivalent.pdf_tex ├── handle-diffeo-homeo-homotopy-equivalent.svg ├── handles-in-dimension-three-s1-x-s2.pdf ├── handles-in-dimension-three-s1-x-s2.pdf_tex ├── handles-in-dimension-three-s1-x-s2.svg ├── handles-in-dimension-two-other-sphere.pdf ├── handles-in-dimension-two-other-sphere.pdf_tex ├── handles-in-dimension-two-other-sphere.svg ├── handles-in-dimension-two-torus-decomposition.pdf ├── handles-in-dimension-two-torus-decomposition.pdf_tex ├── handles-in-dimension-two-torus-decomposition.svg ├── heegaard-splittings-schemattically.pdf ├── heegaard-splittings-schemattically.pdf_tex ├── heegaard-splittings-schemattically.svg ├── homology-definition.pdf ├── homology-definition.pdf_tex ├── homology-definition.svg ├── idea-of-the-proof-maps-a-and-d.pdf ├── idea-of-the-proof-maps-a-and-d.pdf_tex ├── idea-of-the-proof-maps-a-and-d.svg ├── intersection-number.pdf ├── intersection-number.pdf_tex ├── intersection-number.svg ├── intersection-of-manifolds-is-not-always-a-manifold.pdf ├── intersection-of-manifolds-is-not-always-a-manifold.pdf_tex ├── intersection-of-manifolds-is-not-always-a-manifold.svg ├── intersection-points-cancellation.pdf ├── intersection-points-cancellation.pdf_tex ├── intersection-points-cancellation.svg ├── isotopy-between-circle-and-other-circle.pdf ├── isotopy-between-circle-and-other-circle.pdf_tex ├── isotopy-between-circle-and-other-circle.svg ├── kunneth-formula.pdf ├── kunneth-formula.pdf_tex ├── kunneth-formula.svg ├── l-bar-last-condition-of-manifold-with-boundary.pdf ├── l-bar-last-condition-of-manifold-with-boundary.pdf_tex ├── l-bar-last-condition-of-manifold-with-boundary.svg ├── l-bar-manifold-2-dimensional-case-part-flow.pdf ├── l-bar-manifold-2-dimensional-case-part-flow.pdf_tex ├── l-bar-manifold-2-dimensional-case-part-flow.svg ├── l-bar-manifold-2-dimensional-case.pdf ├── l-bar-manifold-2-dimensional-case.pdf_tex ├── l-bar-manifold-2-dimensional-case.svg ├── lbar-manifold-three-dimensional-case.pdf ├── lbar-manifold-three-dimensional-case.pdf_tex ├── lbar-manifold-three-dimensional-case.svg ├── lemma-partial-squared-zero-proof.pdf ├── lemma-partial-squared-zero-proof.pdf_tex ├── lemma-partial-squared-zero-proof.svg ├── lemma-sphere-connect-with-tube-proof.pdf ├── lemma-sphere-connect-with-tube-proof.pdf_tex ├── lemma-sphere-connect-with-tube-proof.svg ├── lemma-sphere-connect-with-tube.pdf ├── lemma-sphere-connect-with-tube.pdf_tex ├── lemma-sphere-connect-with-tube.svg ├── level-sets-of-distance-function-torus.pdf ├── level-sets-of-distance-function-torus.pdf_tex ├── level-sets-of-distance-function-torus.svg ├── linear-map-rank-nullity-theorem.pdf ├── linear-map-rank-nullity-theorem.pdf_tex ├── linear-map-rank-nullity-theorem.svg ├── local-model.pdf ├── local-model.pdf_tex ├── local-model.svg ├── mathcal-m-trajectories-other-sphere-only-m.pdf ├── mathcal-m-trajectories-other-sphere-only-m.pdf_tex ├── mathcal-m-trajectories-other-sphere-only-m.svg ├── mathcal-m-trajectories-other-sphere.pdf ├── mathcal-m-trajectories-other-sphere.pdf_tex ├── mathcal-m-trajectories-other-sphere.svg ├── mayer-vietoris-example.pdf ├── mayer-vietoris-example.pdf_tex ├── mayer-vietoris-example.svg ├── more-concrete-morse-charts.pdf ├── more-concrete-morse-charts.pdf_tex ├── more-concrete-morse-charts.svg ├── mores-homology-three-torus-critical-points-graph.pdf ├── mores-homology-three-torus-critical-points-graph.pdf_tex ├── mores-homology-three-torus-critical-points-graph.svg ├── morse-chain-complex-visualized-truncated.pdf ├── morse-chain-complex-visualized-truncated.pdf_tex ├── morse-chain-complex-visualized-truncated.svg ├── morse-chain-complex-visualized.pdf ├── morse-chain-complex-visualized.pdf_tex ├── morse-chain-complex-visualized.svg ├── morse-chart-flow-lines.pdf ├── morse-chart-flow-lines.pdf_tex ├── morse-chart-flow-lines.svg ├── morse-chart-zoomed-in.pdf ├── morse-chart-zoomed-in.pdf_tex ├── morse-chart-zoomed-in.svg ├── morse-chart.pdf ├── morse-chart.pdf_tex ├── morse-chart.svg ├── morse-complex-is-a-complex-idea-of-proof.pdf ├── morse-complex-is-a-complex-idea-of-proof.pdf_tex ├── morse-complex-is-a-complex-idea-of-proof.svg ├── morse-function-sphere-example.pdf ├── morse-function-sphere-example.pdf_tex ├── morse-function-sphere-example.svg ├── morse-homology-definition-of-topology.pdf ├── morse-homology-definition-of-topology.pdf_tex ├── morse-homology-definition-of-topology.svg ├── morse-homology-independence-cilinder.pdf ├── morse-homology-independence-cilinder.pdf_tex ├── morse-homology-independence-cilinder.svg ├── morse-homology-independence-g-function.pdf ├── morse-homology-independence-g-function.pdf_tex ├── morse-homology-independence-g-function.svg ├── morse-homology-independence-partial-squared-zero-bis.pdf ├── morse-homology-independence-partial-squared-zero-bis.pdf_tex ├── morse-homology-independence-partial-squared-zero-bis.svg ├── morse-homology-independence-partial-squared-zero.pdf ├── morse-homology-independence-partial-squared-zero.pdf_tex ├── morse-homology-independence-partial-squared-zero.svg ├── morse-homology-independence-tube.pdf ├── morse-homology-independence-tube.pdf_tex ├── morse-homology-independence-tube.svg ├── morse-homology-independence-two-dimensional-slide-three-d.pdf ├── morse-homology-independence-two-dimensional-slide-three-d.pdf_tex ├── morse-homology-independence-two-dimensional-slide-three-d.svg ├── morse-homology-independence-two-dimensional-slide.pdf ├── morse-homology-independence-two-dimensional-slide.pdf_tex ├── morse-homology-independence-two-dimensional-slide.svg ├── morse-homology-is-singular-homology-defining-map-a.pdf ├── morse-homology-is-singular-homology-defining-map-a.pdf_tex ├── morse-homology-is-singular-homology-defining-map-a.svg ├── morse-homology-other-sphere-differential.pdf ├── morse-homology-other-sphere-differential.pdf_tex ├── morse-homology-other-sphere-differential.svg ├── morse-homology-three-torus-trajectories.pdf ├── morse-homology-three-torus-trajectories.pdf_tex ├── morse-homology-three-torus-trajectories.svg ├── non-example-of-morse-function.pdf ├── non-example-of-morse-function.pdf_tex ├── non-example-of-morse-function.svg ├── non-examples-of-morse-functions.pdf ├── non-examples-of-morse-functions.pdf_tex ├── non-examples-of-morse-functions.svg ├── one-dimensional-handle-decomposition-examples.pdf ├── one-dimensional-handle-decomposition-examples.pdf_tex ├── one-dimensional-handle-decomposition-examples.svg ├── one-dimensional-reduction.pdf ├── one-dimensional-reduction.pdf_tex ├── one-dimensional-reduction.svg ├── orientation-example.pdf ├── orientation-example.pdf_tex ├── orientation-example.svg ├── other-sphere-and-normal-sphere-morse-complex.pdf ├── other-sphere-and-normal-sphere-morse-complex.pdf_tex ├── other-sphere-and-normal-sphere-morse-complex.svg ├── other-sphere-cancelation-of-critical-points.pdf ├── other-sphere-cancelation-of-critical-points.pdf_tex ├── other-sphere-cancelation-of-critical-points.svg ├── other-sphere-definition-of-mathcal-m.pdf ├── other-sphere-definition-of-mathcal-m.pdf_tex ├── other-sphere-definition-of-mathcal-m.svg ├── other-sphere-morse-complex-modules.pdf ├── other-sphere-morse-complex-modules.pdf_tex ├── other-sphere-morse-complex-modules.svg ├── partial-squared-zero-space-compact.pdf ├── partial-squared-zero-space-compact.pdf_tex ├── partial-squared-zero-space-compact.svg ├── proof-e1-e2-e3-disconnect-case.pdf ├── proof-e1-e2-e3-disconnect-case.pdf_tex ├── proof-e1-e2-e3-disconnect-case.svg ├── proof-of-cobordism-without-critical-points.pdf ├── proof-of-cobordism-without-critical-points.pdf_tex ├── proof-of-cobordism-without-critical-points.svg ├── proof-reordening-properties-of-g.pdf ├── proof-reordening-properties-of-g.pdf_tex ├── proof-reordening-properties-of-g.svg ├── rank-codimension.pdf ├── rank-codimension.pdf_tex ├── reordening-theorem-milnor-h-cobordism.pdf ├── reordening-theorem-milnor-h-cobordism.pdf_tex ├── reordening-theorem-milnor-h-cobordism.svg ├── ricci-flow.pdf ├── ricci-flow.pdf_tex ├── ricci-flow.svg ├── second-cancellation-theorem-example.pdf ├── second-cancellation-theorem-example.pdf_tex ├── second-cancellation-theorem-example.svg ├── second-cancellation-theorem-setup.pdf ├── second-cancellation-theorem-setup.pdf_tex ├── second-cancellation-theorem-setup.svg ├── self-indexing-morse-function-torus-tilted.pdf ├── self-indexing-morse-function-torus-tilted.pdf_tex ├── self-indexing-morse-function-torus-tilted.svg ├── stabilization.pdf ├── stabilization.pdf_tex ├── stabilization.svg ├── stable-and-unstable-manifolds-are-manifiolds.pdf ├── stable-and-unstable-manifolds-are-manifiolds.pdf_tex ├── stable-and-unstable-manifolds-are-manifiolds.svg ├── stable-and-unstable-manifolds-are-manifiolds.svg.2020_12_13_11_17_24.0.pdf ├── stable-and-unstable-manifolds-are-manifiolds.svg.2020_12_13_11_17_24.0.pdf_tex ├── stable-and-unstable-manifolds-are-manifiolds.svg.2020_12_13_11_17_24.0.svg ├── stable-and-unstable-manifolds-are-manifiolds.svg.2020_12_13_11_21_18.0.pdf ├── stable-and-unstable-manifolds-are-manifiolds.svg.2020_12_13_11_21_18.0.pdf_tex ├── stable-and-unstable-manifolds-are-manifiolds.svg.2020_12_13_11_21_18.0.svg ├── test-figure.pdf ├── test-figure.pdf_tex ├── test-figure.svg ├── three-torus-handle-decomposition.pdf ├── three-torus-handle-decomposition.pdf_tex ├── three-torus-handle-decomposition.svg ├── three-torus-heegaard-splitting.pdf ├── three-torus-heegaard-splitting.pdf_tex ├── three-torus-heegaard-splitting.svg ├── tilted-klein-bottle-over-z.pdf ├── tilted-klein-bottle-over-z.pdf_tex ├── tilted-klein-bottle-over-z.svg ├── tilted-torus.pdf ├── tilted-torus.pdf_tex ├── tilted-torus.svg ├── torus-height-function-stable-and-unstable-manifolds.pdf ├── torus-height-function-stable-and-unstable-manifolds.pdf_tex ├── torus-height-function-stable-and-unstable-manifolds.svg ├── torus-homology.pdf ├── torus-homology.pdf_tex ├── torus-homology.svg ├── torus-tilted-height-function-stable-and-unstable-manifolds.pdf ├── torus-tilted-height-function-stable-and-unstable-manifolds.pdf_tex ├── torus-tilted-height-function-stable-and-unstable-manifolds.svg ├── transversality-examples.pdf ├── transversality-examples.pdf_tex ├── transversality-examples.svg ├── when-can-we-attach-multiple-handles-at-the-same-time.pdf ├── when-can-we-attach-multiple-handles-at-the-same-time.pdf_tex ├── when-can-we-attach-multiple-handles-at-the-same-time.svg ├── when-can-we-not-attach-multiple-handles-at-the-same-time.pdf ├── when-can-we-not-attach-multiple-handles-at-the-same-time.pdf_tex ├── when-can-we-not-attach-multiple-handles-at-the-same-time.svg ├── whitneys-theorem-model-isotopy.pdf ├── whitneys-theorem-model-isotopy.pdf_tex ├── whitneys-theorem-model-isotopy.svg ├── whitneys-theorem-proof-model.pdf ├── whitneys-theorem-proof-model.pdf_tex ├── whitneys-theorem-proof-model.svg ├── without-zero-handles.pdf ├── without-zero-handles.pdf_tex └── without-zero-handles.svg ├── kuleuven-template ├── LogoKULeuven.png ├── covers.pdf ├── covers.tex └── sedes.png ├── marginfix.sty ├── master.ptc ├── master.tex ├── notebooks ├── damien.1.4.c.nb └── three-torus │ ├── output.png │ └── three-torus.nb ├── preamble.tex ├── preface.tex ├── scratchpads └── 2020-11-13-Note-16-55.xoj ├── summary.tex ├── symbols.tex ├── todo.tex └── tuftebook.cls /.github/workflows/main.yml: -------------------------------------------------------------------------------- 1 | name: Build LaTeX document 2 | on: [push] 3 | jobs: 4 | build_latex: 5 | runs-on: ubuntu-latest 6 | steps: 7 | - name: Set up Git repository 8 | uses: actions/checkout@v2 9 | - name: Compile LaTeX document 10 | uses: dante-ev/latex-action@latest 11 | with: 12 | working_directory: thesis 13 | root_file: master.tex 14 | - uses: actions/upload-artifact@v2 15 | with: 16 | name: master.pdf 17 | path: thesis/master.pdf 18 | -------------------------------------------------------------------------------- /README.md: -------------------------------------------------------------------------------- 1 | # Master thesis: Morse Theory 2 | 3 | ## *A visual guide from handlebodies to the generalized Poincaré conjecture* 4 | 5 | 6 | I did my masters thesis at KU Leuven in Belgium on Morse theory under the supervision of Charlotte Kirchhoff-Lukat on Morse theory. 7 | 8 | ### Goal 9 | 10 | The goal of the thesis is to state and prove some important results in classical Morse theory, including: 11 | 12 | * Existence of Morse functions 13 | * Handlebody decomposition 14 | * Definition of Morse homology and the fact that it does not depend on the chosen Morse function/gradient vector field 15 | * Morse homology is isomorphic to singular homology 16 | * Morse inequalities 17 | * h-cobordism theorem, from which the higher dimensional Poincaré conjecture follows 18 | 19 | ### Target audience 20 | 21 | The thesis should be accessible to mathematics master students with basic knowledge of differential geometry. To ease the understanding of the geometrical proofs, the thesis also contains more than 100 figures. 22 | 23 | ### Template 24 | 25 | Feel free to use this thesis as a template. It is inspired by the work of Edward Tufte. 26 | ![2021_10_04_001](https://user-images.githubusercontent.com/7069691/135912959-b73f2080-ad53-40d3-bd45-ee54fac604d0.png) 27 | ![2021_10_04_002](https://user-images.githubusercontent.com/7069691/135912965-37c8ddf9-4d93-4c59-9f89-a9fc03d4dd4a.png) 28 | ![2021_10_04_003](https://user-images.githubusercontent.com/7069691/135912973-a7eaceff-9cb8-4dda-ab87-7a19f5358718.png) 29 | 30 | 31 | 32 | 33 | ### Compiling 34 | 35 | Use `latexmk` to compile the thesis: 36 | ```sh 37 | cd thesis 38 | latexmk master.tex 39 | ``` 40 | 41 | Note that I use BibLaTeX (not BibTeX) so be aware of this if you're compiling this with something else than `latexmk`. 42 | -------------------------------------------------------------------------------- /final-version.pdf: -------------------------------------------------------------------------------- https://raw.githubusercontent.com/gillescastel/masterthesis/16b33d4121a8958e624bb0c9157151a63311b119/final-version.pdf -------------------------------------------------------------------------------- /meetings.md: -------------------------------------------------------------------------------- 1 | # Meetings 2 | 3 | ## 2020-10-02 4 | 5 | Initial meeting. 6 | 7 | ## 2020-10-14 8 | 9 | Done: 10 | 11 | * Watched some more Morse videos 12 | - Cancelation of critical points 13 | - Every 3-manifold is boundary of some 4-manifold (under certain conditions) 14 | - Some results needed for Heegaard decompositions 15 | * Watched talk on Floer homology: [Morse homology](https://www.youtube.com/watch?v=hcggpesZ_kA) [Floer homology](https://www.youtube.com/watch?v=SoLPZbLiAVo) 16 | * Made a [dependency chart for the first chapter(s)](https://drive.google.com/file/d/1LSyxkRDMp2VspcCA4x9pddb7uIP2q3kl/view?usp=sharing) 17 | * Wrote a bit (WIP): 18 | - Introduction to transversally 19 | - Morse Lemma 20 | - Existence and abundance 21 | 22 | Selection of discussed topics: 23 | 24 | * Whitney embedding theorem (#3) 25 | * Building manifolds 26 | - Embedding of attaching region up to isotopy 27 | - Collar neighbourhood theorem 28 | * Typo in Audin-Damian? 29 | * Good resources for Heegaard splittings? (#5) 30 | * Building manifolds vs "given a manifold, decompose it" 31 | * Coordinate free / dependent definition of Morse function 32 | * Dehn twists 33 | 34 | Takeaways: 35 | 36 | * Preliminaries should only include things I learnt for this thesis. So e.g. not the definition of a manifold. 37 | * Add page numbers to citations 38 | * Level of detail in proofs should be higher than in books, videos, ... 39 | * Check if there exists an errata for sources 40 | 41 | ## 2020-10-28 42 | 43 | Want to discuss: 44 | 45 | * Doing a PhD at Leuven / ... (what's your experience in Leuven, Cambridge?) 46 | * Compilation problems: using BibLaTeX instead of BiBTeX 47 | * * Google Jamboard? 48 | -------------------------------------------------------------------------------- /questions/proof-cancellation/figures/setup.pdf: -------------------------------------------------------------------------------- https://raw.githubusercontent.com/gillescastel/masterthesis/16b33d4121a8958e624bb0c9157151a63311b119/questions/proof-cancellation/figures/setup.pdf -------------------------------------------------------------------------------- /questions/proof-cancellation/master.tex: -------------------------------------------------------------------------------- 1 | \documentclass[a4paper]{article} 2 | 3 | \usepackage[shortlabels]{enumitem} 4 | \usepackage{float} 5 | \usepackage[utf8]{inputenc} 6 | \usepackage[T1]{fontenc} 7 | \usepackage{textcomp} 8 | \usepackage[dutch]{babel} 9 | \usepackage{amsmath, amssymb} 10 | 11 | 12 | % figure support 13 | \usepackage{import} 14 | \usepackage{xifthen} 15 | \pdfminorversion=7 16 | \usepackage{pdfpages} 17 | \usepackage{transparent} 18 | \newcommand{\incfig}[1]{% 19 | \def\svgwidth{\columnwidth} 20 | \import{./figures/}{#1.pdf_tex} 21 | } 22 | 23 | \newcommand\R{\mathbb R} 24 | \pdfsuppresswarningpagegroup=1 25 | \input{../../thesis/symbols.tex} 26 | 27 | 28 | \begin{document} 29 | Setup: 30 | \begin{itemize} 31 | \item manifold $M$ of dimension $n$ 32 | \item Morse function $M \to \R$ 33 | \item Pseudo-gradient $X$ 34 | \item $p$ and $q$ critical point s with following conditions: 35 | \begin{enumerate}[i)] 36 | \item $\unstable{p}$ and $\stable{q}$ intersect transversely and intersection is made of one orbit $\ell$ of $X$ only, i.e.\ a single gradient flow line from $p$ to $q$. 37 | \item For some $\epsilon > 0$, all gradient flow lines starting at $p$ (that are not $\ell$) crosses the level set $f^{-1}(f(q) - \epsilon)$. 38 | \end{enumerate} 39 | \end{itemize} 40 | 41 | \begin{itemize} 42 | \item Say $\Ind p = k + 1$ and $\Ind q = k$. 43 | \item We are given an open neighborhood $U$ of the closure of $\unstable{p} \cap \{f(q) \le f \le f(p)\} $. 44 | \item After looking at $U \cap \{f = f(q)\} $, we may assume that the frontier of $U$ in $M$ traces a cylinder $C$ tangent to $X$ in the domain $ \{f(q) - \epsilon' \le f \le f(q) + \epsilon'\} $, where $\epsilon' > 0$ satisfies assumption ii) of our theorem. 45 | \end{itemize} 46 | 47 | 48 | \begin{figure}[H] 49 | \centering 50 | \incfig{setup} 51 | \caption{TODO setup} 52 | \label{fig:setup} 53 | \end{figure} 54 | \end{document} 55 | -------------------------------------------------------------------------------- /thesis/chap-outlook.tex: -------------------------------------------------------------------------------- 1 | \chapter*{Outlook} 2 | 3 | As the final chapter of this preliminary report, we would like to give an idea of the possible paths to take in the upcoming semester. 4 | With Chapter 2, we are on the verge of defining the Morse complex. 5 | This is an interesting homology theory that is of a very geometric nature. 6 | While everything initially depends on a choice of Morse function $f$ and pseudo-gradient field $X$, we will prove that the homology that arises is independent. 7 | Even more, we will prove that it is isomorphic to the cellular homology. 8 | 9 | Being geometric, the Morse complex can be used very intuitively for proving important theorems such as the Poincaré duality (by simply replacing $f$ by $-f$), the K\"unneth formula, etc. 10 | We will also prove the Morse inequalities which tell us that the number of index $k$ critical points of a Morse function is bounded from below with $\beta_k$, the $k$-th Betti number. 11 | 12 | We would also want to expand the section on Heegaard splittings as they are a very useful tool for studying $3$-manifolds. We would like to introduce Heegaard diagrams, lens spaces and prove interesting theorems regarding the characterisation of $3$-manifolds. 13 | 14 | Lastly, we will provide the proof of cancellation of two critical points in much more detail. Especially if we would focus on the $h$-cobordism theorem and higher dimensional Poincaré conjecture, this would be relevant. 15 | Another option is to focus on Floer homology and the Arnold conjecture, following the second part of the book of Audin and Damian. 16 | -------------------------------------------------------------------------------- /thesis/conclusion.tex: -------------------------------------------------------------------------------- 1 | \chapter*{Conclusion} 2 | \label{ch:conclusion} 3 | \addcontentsline{toc}{chapter}{\nameref{ch:conclusion}} 4 | 5 | We have started this thesis with an introduction to Morse functions. 6 | While simple, they provide great insight in the structure of differential manifolds, as we have seen. 7 | Morse functions give rise to handlebody decompositions, the Morse complex and eventually Morse homology. 8 | We have shown that Morse homology does not depend on the Morse function nor on the pseudo-gradient vector field and that it is in fact isomorphic to singular homology. 9 | Morse homology gives rise to the Morse inequalities, providing a lower bound for the number of critical points of a Morse function. 10 | 11 | In the last part of the thesis, we have witnessed the power of ideas of Morse. 12 | We have proven multiple cancellation theorems eventually leading to the proof of the minimality of the Morse inequalities, which was originally due to Smale. 13 | This in turn has the $h$-cobordism and the generalized higher dimensional Poincaré conjecture as an immediate corollary, forming the pinnacle of this~thesis. 14 | 15 | As of today, Morse theory remains an important subject in differential geometry. 16 | For example, handlebody decompositions and Heegaard splittings are used extensively for studying $3$- and $4$-manifolds. 17 | Moreover, the ideas of Morse homology have been extended to infinite dimensions by Andreas Floer, resulting in proofs of various versions of the Arnold conjecture. 18 | -------------------------------------------------------------------------------- /thesis/copyright.tex: -------------------------------------------------------------------------------- 1 | \vspace*{\fill} 2 | © Copyright by KU Leuven 3 | 4 | Without written permission of the promotors and the authors it is forbidden to reproduce or adapt in any form or by any means any part of this publication. Requests for obtaining the right to reproduce or utilize parts of this publication should be addressed to KU Leuven, Faculteit Wetenschappen, Celestijnenlaan 200H - bus 2100, 3001 Leuven (Heverlee), Telephone +32 16 32 14 01. 5 | 6 | A written permission of the promotor is also required to use the methods, products, schematics and programs described in this work for industrial or commercial use, and for submitting this publication in scientific contests. 7 | -------------------------------------------------------------------------------- /thesis/figures/.svg: -------------------------------------------------------------------------------- 1 | 2 | 3 | 4 | 19 | 21 | 43 | 51 | 52 | 54 | 55 | 57 | image/svg+xml 58 | 60 | 61 | 62 | 63 | 64 | 69 | 70 | -------------------------------------------------------------------------------- /thesis/figures/a-is-a-chain-map.pdf: -------------------------------------------------------------------------------- https://raw.githubusercontent.com/gillescastel/masterthesis/16b33d4121a8958e624bb0c9157151a63311b119/thesis/figures/a-is-a-chain-map.pdf -------------------------------------------------------------------------------- /thesis/figures/a-is-a-chain-map.pdf_tex: -------------------------------------------------------------------------------- 1 | %% Creator: Inkscape inkscape 0.92.4, www.inkscape.org 2 | %% PDF/EPS/PS + LaTeX output extension by Johan Engelen, 2010 3 | %% Accompanies image file 'a-is-a-chain-map.pdf' (pdf, eps, ps) 4 | %% 5 | %% To include the image in your LaTeX document, write 6 | %% \input{.pdf_tex} 7 | %% instead of 8 | %% \includegraphics{.pdf} 9 | %% To scale the image, write 10 | %% \def\svgwidth{} 11 | %% \input{.pdf_tex} 12 | %% instead of 13 | %% \includegraphics[width=]{.pdf} 14 | %% 15 | %% Images with a different path to the parent latex file can 16 | %% be accessed with the `import' package (which may need to be 17 | %% installed) using 18 | %% \usepackage{import} 19 | %% in the preamble, and then including the image with 20 | %% \import{}{.pdf_tex} 21 | %% Alternatively, one can specify 22 | %% \graphicspath{{/}} 23 | %% 24 | %% For more information, please see info/svg-inkscape on CTAN: 25 | %% http://tug.ctan.org/tex-archive/info/svg-inkscape 26 | %% 27 | \begingroup% 28 | \makeatletter% 29 | \providecommand\color[2][]{% 30 | \errmessage{(Inkscape) Color is used for the text in Inkscape, but the package 'color.sty' is not loaded}% 31 | \renewcommand\color[2][]{}% 32 | }% 33 | \providecommand\transparent[1]{% 34 | \errmessage{(Inkscape) Transparency is used (non-zero) for the text in Inkscape, but the package 'transparent.sty' is not loaded}% 35 | \renewcommand\transparent[1]{}% 36 | }% 37 | \providecommand\rotatebox[2]{#2}% 38 | \newcommand*\fsize{\dimexpr\f@size pt\relax}% 39 | \newcommand*\lineheight[1]{\fontsize{\fsize}{#1\fsize}\selectfont}% 40 | \ifx\svgwidth\undefined% 41 | \setlength{\unitlength}{201.04785829bp}% 42 | \ifx\svgscale\undefined% 43 | \relax% 44 | \else% 45 | \setlength{\unitlength}{\unitlength * \real{\svgscale}}% 46 | \fi% 47 | \else% 48 | \setlength{\unitlength}{\svgwidth}% 49 | \fi% 50 | \global\let\svgwidth\undefined% 51 | \global\let\svgscale\undefined% 52 | \makeatother% 53 | \begin{picture}(1,0.96985137)% 54 | \lineheight{1}% 55 | \setlength\tabcolsep{0pt}% 56 | \put(0,0){\includegraphics[width=\unitlength,page=1]{a-is-a-chain-map.pdf}}% 57 | \put(0.50306763,0.78377407){\color[rgb]{0,0,0}\makebox(0,0)[t]{\lineheight{1.25}\smash{\begin{tabular}[t]{c}$A$\end{tabular}}}}% 58 | \put(0,0){\includegraphics[width=\unitlength,page=2]{a-is-a-chain-map.pdf}}% 59 | \put(0.26056821,0.47050683){\color[rgb]{0,0,0}\makebox(0,0)[lt]{\lineheight{1.25}\smash{\begin{tabular}[t]{l}$\partial$\end{tabular}}}}% 60 | \put(0,0){\includegraphics[width=\unitlength,page=3]{a-is-a-chain-map.pdf}}% 61 | \put(0.76785605,0.47435997){\color[rgb]{0,0,0}\makebox(0,0)[lt]{\lineheight{1.25}\smash{\begin{tabular}[t]{l}$\partial^\text{Morse}$\end{tabular}}}}% 62 | \put(0,0){\includegraphics[width=\unitlength,page=4]{a-is-a-chain-map.pdf}}% 63 | \put(0.50306763,0.19618889){\color[rgb]{0,0,0}\makebox(0,0)[t]{\lineheight{1.25}\smash{\begin{tabular}[t]{c}$A$\end{tabular}}}}% 64 | \put(0,0){\includegraphics[width=\unitlength,page=5]{a-is-a-chain-map.pdf}}% 65 | \end{picture}% 66 | \endgroup% 67 | -------------------------------------------------------------------------------- /thesis/figures/a-is-left-inverse-to-d.pdf: -------------------------------------------------------------------------------- https://raw.githubusercontent.com/gillescastel/masterthesis/16b33d4121a8958e624bb0c9157151a63311b119/thesis/figures/a-is-left-inverse-to-d.pdf -------------------------------------------------------------------------------- /thesis/figures/a-is-left-inverse-to-d.pdf_tex: -------------------------------------------------------------------------------- 1 | %% Creator: Inkscape inkscape 0.92.4, www.inkscape.org 2 | %% PDF/EPS/PS + LaTeX output extension by Johan Engelen, 2010 3 | %% Accompanies image file 'a-is-left-inverse-to-d.pdf' (pdf, eps, ps) 4 | %% 5 | %% To include the image in your LaTeX document, write 6 | %% \input{.pdf_tex} 7 | %% instead of 8 | %% \includegraphics{.pdf} 9 | %% To scale the image, write 10 | %% \def\svgwidth{} 11 | %% \input{.pdf_tex} 12 | %% instead of 13 | %% \includegraphics[width=]{.pdf} 14 | %% 15 | %% Images with a different path to the parent latex file can 16 | %% be accessed with the `import' package (which may need to be 17 | %% installed) using 18 | %% \usepackage{import} 19 | %% in the preamble, and then including the image with 20 | %% \import{}{.pdf_tex} 21 | %% Alternatively, one can specify 22 | %% \graphicspath{{/}} 23 | %% 24 | %% For more information, please see info/svg-inkscape on CTAN: 25 | %% http://tug.ctan.org/tex-archive/info/svg-inkscape 26 | %% 27 | \begingroup% 28 | \makeatletter% 29 | \providecommand\color[2][]{% 30 | \errmessage{(Inkscape) Color is used for the text in Inkscape, but the package 'color.sty' is not loaded}% 31 | \renewcommand\color[2][]{}% 32 | }% 33 | \providecommand\transparent[1]{% 34 | \errmessage{(Inkscape) Transparency is used (non-zero) for the text in Inkscape, but the package 'transparent.sty' is not loaded}% 35 | \renewcommand\transparent[1]{}% 36 | }% 37 | \providecommand\rotatebox[2]{#2}% 38 | \newcommand*\fsize{\dimexpr\f@size pt\relax}% 39 | \newcommand*\lineheight[1]{\fontsize{\fsize}{#1\fsize}\selectfont}% 40 | \ifx\svgwidth\undefined% 41 | \setlength{\unitlength}{259.17645552bp}% 42 | \ifx\svgscale\undefined% 43 | \relax% 44 | \else% 45 | \setlength{\unitlength}{\unitlength * \real{\svgscale}}% 46 | \fi% 47 | \else% 48 | \setlength{\unitlength}{\svgwidth}% 49 | \fi% 50 | \global\let\svgwidth\undefined% 51 | \global\let\svgscale\undefined% 52 | \makeatother% 53 | \begin{picture}(1,0.28225314)% 54 | \lineheight{1}% 55 | \setlength\tabcolsep{0pt}% 56 | \put(0,0){\includegraphics[width=\unitlength,page=1]{a-is-left-inverse-to-d.pdf}}% 57 | \put(0.30721839,0.14307304){\color[rgb]{0,0,0}\makebox(0,0)[t]{\lineheight{1.25}\smash{\begin{tabular}[t]{c}$D$\end{tabular}}}}% 58 | \put(0,0){\includegraphics[width=\unitlength,page=2]{a-is-left-inverse-to-d.pdf}}% 59 | \put(0.69803622,0.14307304){\color[rgb]{0,0,0}\makebox(0,0)[t]{\lineheight{1.25}\smash{\begin{tabular}[t]{c}$A$\end{tabular}}}}% 60 | \end{picture}% 61 | \endgroup% 62 | -------------------------------------------------------------------------------- /thesis/figures/abundance-of-morse-functions-parametrization-of-the-normal-bundle.pdf: -------------------------------------------------------------------------------- https://raw.githubusercontent.com/gillescastel/masterthesis/16b33d4121a8958e624bb0c9157151a63311b119/thesis/figures/abundance-of-morse-functions-parametrization-of-the-normal-bundle.pdf -------------------------------------------------------------------------------- /thesis/figures/addition-of-columns-geometrically.pdf: -------------------------------------------------------------------------------- https://raw.githubusercontent.com/gillescastel/masterthesis/16b33d4121a8958e624bb0c9157151a63311b119/thesis/figures/addition-of-columns-geometrically.pdf -------------------------------------------------------------------------------- /thesis/figures/alteration-of-pseudogradient-vector-field.pdf: -------------------------------------------------------------------------------- https://raw.githubusercontent.com/gillescastel/masterthesis/16b33d4121a8958e624bb0c9157151a63311b119/thesis/figures/alteration-of-pseudogradient-vector-field.pdf -------------------------------------------------------------------------------- /thesis/figures/alteration-of-vector-field.pdf: -------------------------------------------------------------------------------- https://raw.githubusercontent.com/gillescastel/masterthesis/16b33d4121a8958e624bb0c9157151a63311b119/thesis/figures/alteration-of-vector-field.pdf -------------------------------------------------------------------------------- /thesis/figures/any-closed-manifold-admits-a-handlebody-decomposition.pdf: -------------------------------------------------------------------------------- https://raw.githubusercontent.com/gillescastel/masterthesis/16b33d4121a8958e624bb0c9157151a63311b119/thesis/figures/any-closed-manifold-admits-a-handlebody-decomposition.pdf -------------------------------------------------------------------------------- /thesis/figures/approximate-morse-functions.pdf: -------------------------------------------------------------------------------- https://raw.githubusercontent.com/gillescastel/masterthesis/16b33d4121a8958e624bb0c9157151a63311b119/thesis/figures/approximate-morse-functions.pdf -------------------------------------------------------------------------------- /thesis/figures/assertion-1.pdf: -------------------------------------------------------------------------------- https://raw.githubusercontent.com/gillescastel/masterthesis/16b33d4121a8958e624bb0c9157151a63311b119/thesis/figures/assertion-1.pdf -------------------------------------------------------------------------------- /thesis/figures/assertion-1.pdf_tex: -------------------------------------------------------------------------------- 1 | %% Creator: Inkscape inkscape 0.92.4, www.inkscape.org 2 | %% PDF/EPS/PS + LaTeX output extension by Johan Engelen, 2010 3 | %% Accompanies image file 'assertion-1.pdf' (pdf, eps, ps) 4 | %% 5 | %% To include the image in your LaTeX document, write 6 | %% \input{.pdf_tex} 7 | %% instead of 8 | %% \includegraphics{.pdf} 9 | %% To scale the image, write 10 | %% \def\svgwidth{} 11 | %% \input{.pdf_tex} 12 | %% instead of 13 | %% \includegraphics[width=]{.pdf} 14 | %% 15 | %% Images with a different path to the parent latex file can 16 | %% be accessed with the `import' package (which may need to be 17 | %% installed) using 18 | %% \usepackage{import} 19 | %% in the preamble, and then including the image with 20 | %% \import{}{.pdf_tex} 21 | %% Alternatively, one can specify 22 | %% \graphicspath{{/}} 23 | %% 24 | %% For more information, please see info/svg-inkscape on CTAN: 25 | %% http://tug.ctan.org/tex-archive/info/svg-inkscape 26 | %% 27 | \begingroup% 28 | \makeatletter% 29 | \providecommand\color[2][]{% 30 | \errmessage{(Inkscape) Color is used for the text in Inkscape, but the package 'color.sty' is not loaded}% 31 | \renewcommand\color[2][]{}% 32 | }% 33 | \providecommand\transparent[1]{% 34 | \errmessage{(Inkscape) Transparency is used (non-zero) for the text in Inkscape, but the package 'transparent.sty' is not loaded}% 35 | \renewcommand\transparent[1]{}% 36 | }% 37 | \providecommand\rotatebox[2]{#2}% 38 | \newcommand*\fsize{\dimexpr\f@size pt\relax}% 39 | \newcommand*\lineheight[1]{\fontsize{\fsize}{#1\fsize}\selectfont}% 40 | \ifx\svgwidth\undefined% 41 | \setlength{\unitlength}{680.31496063bp}% 42 | \ifx\svgscale\undefined% 43 | \relax% 44 | \else% 45 | \setlength{\unitlength}{\unitlength * \real{\svgscale}}% 46 | \fi% 47 | \else% 48 | \setlength{\unitlength}{\svgwidth}% 49 | \fi% 50 | \global\let\svgwidth\undefined% 51 | \global\let\svgscale\undefined% 52 | \makeatother% 53 | \begin{picture}(1,0.5)% 54 | \lineheight{1}% 55 | \setlength\tabcolsep{0pt}% 56 | \end{picture}% 57 | \endgroup% 58 | -------------------------------------------------------------------------------- /thesis/figures/assertion-1.svg: -------------------------------------------------------------------------------- 1 | 2 | 3 | 4 | 19 | 21 | 43 | 51 | 52 | 54 | 55 | 57 | image/svg+xml 58 | 60 | 61 | 62 | 63 | 64 | 69 | 70 | -------------------------------------------------------------------------------- /thesis/figures/assertion-4.pdf: -------------------------------------------------------------------------------- https://raw.githubusercontent.com/gillescastel/masterthesis/16b33d4121a8958e624bb0c9157151a63311b119/thesis/figures/assertion-4.pdf -------------------------------------------------------------------------------- /thesis/figures/assertion-5.pdf: -------------------------------------------------------------------------------- https://raw.githubusercontent.com/gillescastel/masterthesis/16b33d4121a8958e624bb0c9157151a63311b119/thesis/figures/assertion-5.pdf -------------------------------------------------------------------------------- /thesis/figures/bigger-figure.pdf: -------------------------------------------------------------------------------- https://raw.githubusercontent.com/gillescastel/masterthesis/16b33d4121a8958e624bb0c9157151a63311b119/thesis/figures/bigger-figure.pdf -------------------------------------------------------------------------------- /thesis/figures/bigger-figure.pdf_tex: -------------------------------------------------------------------------------- 1 | %% Creator: Inkscape inkscape 0.92.4, www.inkscape.org 2 | %% PDF/EPS/PS + LaTeX output extension by Johan Engelen, 2010 3 | %% Accompanies image file 'bigger-figure.pdf' (pdf, eps, ps) 4 | %% 5 | %% To include the image in your LaTeX document, write 6 | %% \input{.pdf_tex} 7 | %% instead of 8 | %% \includegraphics{.pdf} 9 | %% To scale the image, write 10 | %% \def\svgwidth{} 11 | %% \input{.pdf_tex} 12 | %% instead of 13 | %% \includegraphics[width=]{.pdf} 14 | %% 15 | %% Images with a different path to the parent latex file can 16 | %% be accessed with the `import' package (which may need to be 17 | %% installed) using 18 | %% \usepackage{import} 19 | %% in the preamble, and then including the image with 20 | %% \import{}{.pdf_tex} 21 | %% Alternatively, one can specify 22 | %% \graphicspath{{/}} 23 | %% 24 | %% For more information, please see info/svg-inkscape on CTAN: 25 | %% http://tug.ctan.org/tex-archive/info/svg-inkscape 26 | %% 27 | \begingroup% 28 | \makeatletter% 29 | \providecommand\color[2][]{% 30 | \errmessage{(Inkscape) Color is used for the text in Inkscape, but the package 'color.sty' is not loaded}% 31 | \renewcommand\color[2][]{}% 32 | }% 33 | \providecommand\transparent[1]{% 34 | \errmessage{(Inkscape) Transparency is used (non-zero) for the text in Inkscape, but the package 'transparent.sty' is not loaded}% 35 | \renewcommand\transparent[1]{}% 36 | }% 37 | \providecommand\rotatebox[2]{#2}% 38 | \newcommand*\fsize{\dimexpr\f@size pt\relax}% 39 | \newcommand*\lineheight[1]{\fontsize{\fsize}{#1\fsize}\selectfont}% 40 | \ifx\svgwidth\undefined% 41 | \setlength{\unitlength}{680.31496063bp}% 42 | \ifx\svgscale\undefined% 43 | \relax% 44 | \else% 45 | \setlength{\unitlength}{\unitlength * \real{\svgscale}}% 46 | \fi% 47 | \else% 48 | \setlength{\unitlength}{\svgwidth}% 49 | \fi% 50 | \global\let\svgwidth\undefined% 51 | \global\let\svgscale\undefined% 52 | \makeatother% 53 | \begin{picture}(1,0.5)% 54 | \lineheight{1}% 55 | \setlength\tabcolsep{0pt}% 56 | \put(0,0){\includegraphics[width=\unitlength,page=1]{bigger-figure.pdf}}% 57 | \end{picture}% 58 | \endgroup% 59 | -------------------------------------------------------------------------------- /thesis/figures/canellation-of-critical-points-situation.pdf: -------------------------------------------------------------------------------- https://raw.githubusercontent.com/gillescastel/masterthesis/16b33d4121a8958e624bb0c9157151a63311b119/thesis/figures/canellation-of-critical-points-situation.pdf -------------------------------------------------------------------------------- /thesis/figures/chain-homotopy-between-d-na-a-and-id.pdf: -------------------------------------------------------------------------------- https://raw.githubusercontent.com/gillescastel/masterthesis/16b33d4121a8958e624bb0c9157151a63311b119/thesis/figures/chain-homotopy-between-d-na-a-and-id.pdf -------------------------------------------------------------------------------- /thesis/figures/changing-one-handles-in-three-handles.pdf: -------------------------------------------------------------------------------- https://raw.githubusercontent.com/gillescastel/masterthesis/16b33d4121a8958e624bb0c9157151a63311b119/thesis/figures/changing-one-handles-in-three-handles.pdf -------------------------------------------------------------------------------- /thesis/figures/codimensions-transverse.pdf: -------------------------------------------------------------------------------- https://raw.githubusercontent.com/gillescastel/masterthesis/16b33d4121a8958e624bb0c9157151a63311b119/thesis/figures/codimensions-transverse.pdf -------------------------------------------------------------------------------- /thesis/figures/compactification-of-unstable-manifolds.pdf: -------------------------------------------------------------------------------- https://raw.githubusercontent.com/gillescastel/masterthesis/16b33d4121a8958e624bb0c9157151a63311b119/thesis/figures/compactification-of-unstable-manifolds.pdf -------------------------------------------------------------------------------- /thesis/figures/connected-sum-homotopy-spheres.pdf: -------------------------------------------------------------------------------- https://raw.githubusercontent.com/gillescastel/masterthesis/16b33d4121a8958e624bb0c9157151a63311b119/thesis/figures/connected-sum-homotopy-spheres.pdf -------------------------------------------------------------------------------- /thesis/figures/d-is-a-chain-map.pdf: -------------------------------------------------------------------------------- https://raw.githubusercontent.com/gillescastel/masterthesis/16b33d4121a8958e624bb0c9157151a63311b119/thesis/figures/d-is-a-chain-map.pdf -------------------------------------------------------------------------------- /thesis/figures/d-is-a-chain-map.pdf_tex: -------------------------------------------------------------------------------- 1 | %% Creator: Inkscape inkscape 0.92.4, www.inkscape.org 2 | %% PDF/EPS/PS + LaTeX output extension by Johan Engelen, 2010 3 | %% Accompanies image file 'd-is-a-chain-map.pdf' (pdf, eps, ps) 4 | %% 5 | %% To include the image in your LaTeX document, write 6 | %% \input{.pdf_tex} 7 | %% instead of 8 | %% \includegraphics{.pdf} 9 | %% To scale the image, write 10 | %% \def\svgwidth{} 11 | %% \input{.pdf_tex} 12 | %% instead of 13 | %% \includegraphics[width=]{.pdf} 14 | %% 15 | %% Images with a different path to the parent latex file can 16 | %% be accessed with the `import' package (which may need to be 17 | %% installed) using 18 | %% \usepackage{import} 19 | %% in the preamble, and then including the image with 20 | %% \import{}{.pdf_tex} 21 | %% Alternatively, one can specify 22 | %% \graphicspath{{/}} 23 | %% 24 | %% For more information, please see info/svg-inkscape on CTAN: 25 | %% http://tug.ctan.org/tex-archive/info/svg-inkscape 26 | %% 27 | \begingroup% 28 | \makeatletter% 29 | \providecommand\color[2][]{% 30 | \errmessage{(Inkscape) Color is used for the text in Inkscape, but the package 'color.sty' is not loaded}% 31 | \renewcommand\color[2][]{}% 32 | }% 33 | \providecommand\transparent[1]{% 34 | \errmessage{(Inkscape) Transparency is used (non-zero) for the text in Inkscape, but the package 'transparent.sty' is not loaded}% 35 | \renewcommand\transparent[1]{}% 36 | }% 37 | \providecommand\rotatebox[2]{#2}% 38 | \newcommand*\fsize{\dimexpr\f@size pt\relax}% 39 | \newcommand*\lineheight[1]{\fontsize{\fsize}{#1\fsize}\selectfont}% 40 | \ifx\svgwidth\undefined% 41 | \setlength{\unitlength}{200.64975528bp}% 42 | \ifx\svgscale\undefined% 43 | \relax% 44 | \else% 45 | \setlength{\unitlength}{\unitlength * \real{\svgscale}}% 46 | \fi% 47 | \else% 48 | \setlength{\unitlength}{\svgwidth}% 49 | \fi% 50 | \global\let\svgwidth\undefined% 51 | \global\let\svgscale\undefined% 52 | \makeatother% 53 | \begin{picture}(1,0.96979155)% 54 | \lineheight{1}% 55 | \setlength\tabcolsep{0pt}% 56 | \put(0,0){\includegraphics[width=\unitlength,page=1]{d-is-a-chain-map.pdf}}% 57 | \put(0.50307377,0.78433684){\color[rgb]{0,0,0}\makebox(0,0)[t]{\lineheight{1.25}\smash{\begin{tabular}[t]{c}$D$\end{tabular}}}}% 58 | \put(0,0){\includegraphics[width=\unitlength,page=2]{d-is-a-chain-map.pdf}}% 59 | \put(0.2600932,0.47044834){\color[rgb]{0,0,0}\makebox(0,0)[lt]{\lineheight{1.25}\smash{\begin{tabular}[t]{l}$\partial^{\text{Morse}}$\end{tabular}}}}% 60 | \put(0,0){\includegraphics[width=\unitlength,page=3]{d-is-a-chain-map.pdf}}% 61 | \put(0.7683875,0.47430934){\color[rgb]{0,0,0}\makebox(0,0)[lt]{\lineheight{1.25}\smash{\begin{tabular}[t]{l}$\partial$\end{tabular}}}}% 62 | \put(0,0){\includegraphics[width=\unitlength,page=4]{d-is-a-chain-map.pdf}}% 63 | \put(0.50307377,0.19558584){\color[rgb]{0,0,0}\makebox(0,0)[t]{\lineheight{1.25}\smash{\begin{tabular}[t]{c}$D$\end{tabular}}}}% 64 | \put(0,0){\includegraphics[width=\unitlength,page=5]{d-is-a-chain-map.pdf}}% 65 | \end{picture}% 66 | \endgroup% 67 | -------------------------------------------------------------------------------- /thesis/figures/d-na-a-is-not-identity.pdf: -------------------------------------------------------------------------------- https://raw.githubusercontent.com/gillescastel/masterthesis/16b33d4121a8958e624bb0c9157151a63311b119/thesis/figures/d-na-a-is-not-identity.pdf -------------------------------------------------------------------------------- /thesis/figures/d-na-a-is-not-identity.pdf_tex: -------------------------------------------------------------------------------- 1 | %% Creator: Inkscape inkscape 0.92.4, www.inkscape.org 2 | %% PDF/EPS/PS + LaTeX output extension by Johan Engelen, 2010 3 | %% Accompanies image file 'd-na-a-is-not-identity.pdf' (pdf, eps, ps) 4 | %% 5 | %% To include the image in your LaTeX document, write 6 | %% \input{.pdf_tex} 7 | %% instead of 8 | %% \includegraphics{.pdf} 9 | %% To scale the image, write 10 | %% \def\svgwidth{} 11 | %% \input{.pdf_tex} 12 | %% instead of 13 | %% \includegraphics[width=]{.pdf} 14 | %% 15 | %% Images with a different path to the parent latex file can 16 | %% be accessed with the `import' package (which may need to be 17 | %% installed) using 18 | %% \usepackage{import} 19 | %% in the preamble, and then including the image with 20 | %% \import{}{.pdf_tex} 21 | %% Alternatively, one can specify 22 | %% \graphicspath{{/}} 23 | %% 24 | %% For more information, please see info/svg-inkscape on CTAN: 25 | %% http://tug.ctan.org/tex-archive/info/svg-inkscape 26 | %% 27 | \begingroup% 28 | \makeatletter% 29 | \providecommand\color[2][]{% 30 | \errmessage{(Inkscape) Color is used for the text in Inkscape, but the package 'color.sty' is not loaded}% 31 | \renewcommand\color[2][]{}% 32 | }% 33 | \providecommand\transparent[1]{% 34 | \errmessage{(Inkscape) Transparency is used (non-zero) for the text in Inkscape, but the package 'transparent.sty' is not loaded}% 35 | \renewcommand\transparent[1]{}% 36 | }% 37 | \providecommand\rotatebox[2]{#2}% 38 | \newcommand*\fsize{\dimexpr\f@size pt\relax}% 39 | \newcommand*\lineheight[1]{\fontsize{\fsize}{#1\fsize}\selectfont}% 40 | \ifx\svgwidth\undefined% 41 | \setlength{\unitlength}{260.09407344bp}% 42 | \ifx\svgscale\undefined% 43 | \relax% 44 | \else% 45 | \setlength{\unitlength}{\unitlength * \real{\svgscale}}% 46 | \fi% 47 | \else% 48 | \setlength{\unitlength}{\svgwidth}% 49 | \fi% 50 | \global\let\svgwidth\undefined% 51 | \global\let\svgscale\undefined% 52 | \makeatother% 53 | \begin{picture}(1,0.70533506)% 54 | \lineheight{1}% 55 | \setlength\tabcolsep{0pt}% 56 | \put(0,0){\includegraphics[width=\unitlength,page=1]{d-na-a-is-not-identity.pdf}}% 57 | \put(0.30567838,0.53798615){\color[rgb]{0,0,0}\makebox(0,0)[t]{\lineheight{1.25}\smash{\begin{tabular}[t]{c}$A$\end{tabular}}}}% 58 | \put(0,0){\includegraphics[width=\unitlength,page=2]{d-na-a-is-not-identity.pdf}}% 59 | \put(0.69511739,0.53798615){\color[rgb]{0,0,0}\makebox(0,0)[t]{\lineheight{1.25}\smash{\begin{tabular}[t]{c}$D$\end{tabular}}}}% 60 | \put(0,0){\includegraphics[width=\unitlength,page=3]{d-na-a-is-not-identity.pdf}}% 61 | \put(0.30567838,0.14838547){\color[rgb]{0,0,0}\makebox(0,0)[t]{\lineheight{1.25}\smash{\begin{tabular}[t]{c}$A$\end{tabular}}}}% 62 | \put(0,0){\includegraphics[width=\unitlength,page=4]{d-na-a-is-not-identity.pdf}}% 63 | \put(0.69511739,0.14838547){\color[rgb]{0,0,0}\makebox(0,0)[t]{\lineheight{1.25}\smash{\begin{tabular}[t]{c}$D$\end{tabular}}}}% 64 | \put(0,0){\includegraphics[width=\unitlength,page=5]{d-na-a-is-not-identity.pdf}}% 65 | \end{picture}% 66 | \endgroup% 67 | -------------------------------------------------------------------------------- /thesis/figures/definition-boundary-singular-homology.pdf: -------------------------------------------------------------------------------- https://raw.githubusercontent.com/gillescastel/masterthesis/16b33d4121a8958e624bb0c9157151a63311b119/thesis/figures/definition-boundary-singular-homology.pdf -------------------------------------------------------------------------------- /thesis/figures/definition-homotopy-groups.pdf: -------------------------------------------------------------------------------- https://raw.githubusercontent.com/gillescastel/masterthesis/16b33d4121a8958e624bb0c9157151a63311b119/thesis/figures/definition-homotopy-groups.pdf -------------------------------------------------------------------------------- /thesis/figures/definition-homotopy-groups.pdf_tex: -------------------------------------------------------------------------------- 1 | %% Creator: Inkscape inkscape 0.92.4, www.inkscape.org 2 | %% PDF/EPS/PS + LaTeX output extension by Johan Engelen, 2010 3 | %% Accompanies image file 'definition-homotopy-groups.pdf' (pdf, eps, ps) 4 | %% 5 | %% To include the image in your LaTeX document, write 6 | %% \input{.pdf_tex} 7 | %% instead of 8 | %% \includegraphics{.pdf} 9 | %% To scale the image, write 10 | %% \def\svgwidth{} 11 | %% \input{.pdf_tex} 12 | %% instead of 13 | %% \includegraphics[width=]{.pdf} 14 | %% 15 | %% Images with a different path to the parent latex file can 16 | %% be accessed with the `import' package (which may need to be 17 | %% installed) using 18 | %% \usepackage{import} 19 | %% in the preamble, and then including the image with 20 | %% \import{}{.pdf_tex} 21 | %% Alternatively, one can specify 22 | %% \graphicspath{{/}} 23 | %% 24 | %% For more information, please see info/svg-inkscape on CTAN: 25 | %% http://tug.ctan.org/tex-archive/info/svg-inkscape 26 | %% 27 | \begingroup% 28 | \makeatletter% 29 | \providecommand\color[2][]{% 30 | \errmessage{(Inkscape) Color is used for the text in Inkscape, but the package 'color.sty' is not loaded}% 31 | \renewcommand\color[2][]{}% 32 | }% 33 | \providecommand\transparent[1]{% 34 | \errmessage{(Inkscape) Transparency is used (non-zero) for the text in Inkscape, but the package 'transparent.sty' is not loaded}% 35 | \renewcommand\transparent[1]{}% 36 | }% 37 | \providecommand\rotatebox[2]{#2}% 38 | \newcommand*\fsize{\dimexpr\f@size pt\relax}% 39 | \newcommand*\lineheight[1]{\fontsize{\fsize}{#1\fsize}\selectfont}% 40 | \ifx\svgwidth\undefined% 41 | \setlength{\unitlength}{201.33503831bp}% 42 | \ifx\svgscale\undefined% 43 | \relax% 44 | \else% 45 | \setlength{\unitlength}{\unitlength * \real{\svgscale}}% 46 | \fi% 47 | \else% 48 | \setlength{\unitlength}{\svgwidth}% 49 | \fi% 50 | \global\let\svgwidth\undefined% 51 | \global\let\svgscale\undefined% 52 | \makeatother% 53 | \begin{picture}(1,0.7814599)% 54 | \lineheight{1}% 55 | \setlength\tabcolsep{0pt}% 56 | \put(0,0){\includegraphics[width=\unitlength,page=1]{definition-homotopy-groups.pdf}}% 57 | \put(0.33995803,0.21434425){\color[rgb]{0,0,0}\makebox(0,0)[lt]{\lineheight{1.25}\smash{\begin{tabular}[t]{l}$p$\end{tabular}}}}% 58 | \put(0,0){\includegraphics[width=\unitlength,page=2]{definition-homotopy-groups.pdf}}% 59 | \put(0.13135108,0.38068221){\color[rgb]{0,0,0}\makebox(0,0)[lt]{\lineheight{1.25}\smash{\begin{tabular}[t]{l}$\phi$\end{tabular}}}}% 60 | \put(0.7900185,0.60063628){\color[rgb]{0,0,0}\makebox(0,0)[lt]{\lineheight{1.25}\smash{\begin{tabular}[t]{l}$\rho$\end{tabular}}}}% 61 | \put(0.81253475,0.36553997){\color[rgb]{0,0,0}\makebox(0,0)[lt]{\lineheight{1.25}\smash{\begin{tabular}[t]{l}$\sigma$\end{tabular}}}}% 62 | \end{picture}% 63 | \endgroup% 64 | -------------------------------------------------------------------------------- /thesis/figures/definition-relative-homology.pdf: -------------------------------------------------------------------------------- https://raw.githubusercontent.com/gillescastel/masterthesis/16b33d4121a8958e624bb0c9157151a63311b119/thesis/figures/definition-relative-homology.pdf -------------------------------------------------------------------------------- /thesis/figures/definition-relative-homology.pdf_tex: -------------------------------------------------------------------------------- 1 | %% Creator: Inkscape inkscape 0.92.4, www.inkscape.org 2 | %% PDF/EPS/PS + LaTeX output extension by Johan Engelen, 2010 3 | %% Accompanies image file 'definition-relative-homology.pdf' (pdf, eps, ps) 4 | %% 5 | %% To include the image in your LaTeX document, write 6 | %% \input{.pdf_tex} 7 | %% instead of 8 | %% \includegraphics{.pdf} 9 | %% To scale the image, write 10 | %% \def\svgwidth{} 11 | %% \input{.pdf_tex} 12 | %% instead of 13 | %% \includegraphics[width=]{.pdf} 14 | %% 15 | %% Images with a different path to the parent latex file can 16 | %% be accessed with the `import' package (which may need to be 17 | %% installed) using 18 | %% \usepackage{import} 19 | %% in the preamble, and then including the image with 20 | %% \import{}{.pdf_tex} 21 | %% Alternatively, one can specify 22 | %% \graphicspath{{/}} 23 | %% 24 | %% For more information, please see info/svg-inkscape on CTAN: 25 | %% http://tug.ctan.org/tex-archive/info/svg-inkscape 26 | %% 27 | \begingroup% 28 | \makeatletter% 29 | \providecommand\color[2][]{% 30 | \errmessage{(Inkscape) Color is used for the text in Inkscape, but the package 'color.sty' is not loaded}% 31 | \renewcommand\color[2][]{}% 32 | }% 33 | \providecommand\transparent[1]{% 34 | \errmessage{(Inkscape) Transparency is used (non-zero) for the text in Inkscape, but the package 'transparent.sty' is not loaded}% 35 | \renewcommand\transparent[1]{}% 36 | }% 37 | \providecommand\rotatebox[2]{#2}% 38 | \newcommand*\fsize{\dimexpr\f@size pt\relax}% 39 | \newcommand*\lineheight[1]{\fontsize{\fsize}{#1\fsize}\selectfont}% 40 | \ifx\svgwidth\undefined% 41 | \setlength{\unitlength}{111.29285557bp}% 42 | \ifx\svgscale\undefined% 43 | \relax% 44 | \else% 45 | \setlength{\unitlength}{\unitlength * \real{\svgscale}}% 46 | \fi% 47 | \else% 48 | \setlength{\unitlength}{\svgwidth}% 49 | \fi% 50 | \global\let\svgwidth\undefined% 51 | \global\let\svgscale\undefined% 52 | \makeatother% 53 | \begin{picture}(1,0.53576838)% 54 | \lineheight{1}% 55 | \setlength\tabcolsep{0pt}% 56 | \put(0,0){\includegraphics[width=\unitlength,page=1]{definition-relative-homology.pdf}}% 57 | \put(0.46090359,0.40458956){\color[rgb]{0,0,0}\makebox(0,0)[lt]{\lineheight{1.25}\smash{\begin{tabular}[t]{l}$M$\end{tabular}}}}% 58 | \put(0.83356241,0.07820313){\color[rgb]{0,0,0}\makebox(0,0)[lt]{\lineheight{1.25}\smash{\begin{tabular}[t]{l}$\partial M$\end{tabular}}}}% 59 | \put(0.53881556,0.27299249){\color[rgb]{0,0,0}\makebox(0,0)[lt]{\lineheight{1.25}\smash{\begin{tabular}[t]{l}$\sigma$\end{tabular}}}}% 60 | \end{picture}% 61 | \endgroup% 62 | -------------------------------------------------------------------------------- /thesis/figures/definition-symplex.pdf: -------------------------------------------------------------------------------- https://raw.githubusercontent.com/gillescastel/masterthesis/16b33d4121a8958e624bb0c9157151a63311b119/thesis/figures/definition-symplex.pdf -------------------------------------------------------------------------------- /thesis/figures/example-cancelling-handles-in-three-dimensions.pdf: -------------------------------------------------------------------------------- https://raw.githubusercontent.com/gillescastel/masterthesis/16b33d4121a8958e624bb0c9157151a63311b119/thesis/figures/example-cancelling-handles-in-three-dimensions.pdf -------------------------------------------------------------------------------- /thesis/figures/example-cancelling-handles-in-three-dimensions.pdf_tex: -------------------------------------------------------------------------------- 1 | %% Creator: Inkscape inkscape 0.92.4, www.inkscape.org 2 | %% PDF/EPS/PS + LaTeX output extension by Johan Engelen, 2010 3 | %% Accompanies image file 'example-cancelling-handles-in-three-dimensions.pdf' (pdf, eps, ps) 4 | %% 5 | %% To include the image in your LaTeX document, write 6 | %% \input{.pdf_tex} 7 | %% instead of 8 | %% \includegraphics{.pdf} 9 | %% To scale the image, write 10 | %% \def\svgwidth{} 11 | %% \input{.pdf_tex} 12 | %% instead of 13 | %% \includegraphics[width=]{.pdf} 14 | %% 15 | %% Images with a different path to the parent latex file can 16 | %% be accessed with the `import' package (which may need to be 17 | %% installed) using 18 | %% \usepackage{import} 19 | %% in the preamble, and then including the image with 20 | %% \import{}{.pdf_tex} 21 | %% Alternatively, one can specify 22 | %% \graphicspath{{/}} 23 | %% 24 | %% For more information, please see info/svg-inkscape on CTAN: 25 | %% http://tug.ctan.org/tex-archive/info/svg-inkscape 26 | %% 27 | \begingroup% 28 | \makeatletter% 29 | \providecommand\color[2][]{% 30 | \errmessage{(Inkscape) Color is used for the text in Inkscape, but the package 'color.sty' is not loaded}% 31 | \renewcommand\color[2][]{}% 32 | }% 33 | \providecommand\transparent[1]{% 34 | \errmessage{(Inkscape) Transparency is used (non-zero) for the text in Inkscape, but the package 'transparent.sty' is not loaded}% 35 | \renewcommand\transparent[1]{}% 36 | }% 37 | \providecommand\rotatebox[2]{#2}% 38 | \newcommand*\fsize{\dimexpr\f@size pt\relax}% 39 | \newcommand*\lineheight[1]{\fontsize{\fsize}{#1\fsize}\selectfont}% 40 | \ifx\svgwidth\undefined% 41 | \setlength{\unitlength}{196.11246665bp}% 42 | \ifx\svgscale\undefined% 43 | \relax% 44 | \else% 45 | \setlength{\unitlength}{\unitlength * \real{\svgscale}}% 46 | \fi% 47 | \else% 48 | \setlength{\unitlength}{\svgwidth}% 49 | \fi% 50 | \global\let\svgwidth\undefined% 51 | \global\let\svgscale\undefined% 52 | \makeatother% 53 | \begin{picture}(1,0.51116888)% 54 | \lineheight{1}% 55 | \setlength\tabcolsep{0pt}% 56 | \put(0,0){\includegraphics[width=\unitlength,page=1]{example-cancelling-handles-in-three-dimensions.pdf}}% 57 | \end{picture}% 58 | \endgroup% 59 | -------------------------------------------------------------------------------- /thesis/figures/example-when-fp-is-not-a-morse-function.pdf: -------------------------------------------------------------------------------- https://raw.githubusercontent.com/gillescastel/masterthesis/16b33d4121a8958e624bb0c9157151a63311b119/thesis/figures/example-when-fp-is-not-a-morse-function.pdf -------------------------------------------------------------------------------- /thesis/figures/example-when-fp-is-not-a-morse-function.pdf_tex: -------------------------------------------------------------------------------- 1 | %% Creator: Inkscape inkscape 0.92.4, www.inkscape.org 2 | %% PDF/EPS/PS + LaTeX output extension by Johan Engelen, 2010 3 | %% Accompanies image file 'example-when-fp-is-not-a-morse-function.pdf' (pdf, eps, ps) 4 | %% 5 | %% To include the image in your LaTeX document, write 6 | %% \input{.pdf_tex} 7 | %% instead of 8 | %% \includegraphics{.pdf} 9 | %% To scale the image, write 10 | %% \def\svgwidth{} 11 | %% \input{.pdf_tex} 12 | %% instead of 13 | %% \includegraphics[width=]{.pdf} 14 | %% 15 | %% Images with a different path to the parent latex file can 16 | %% be accessed with the `import' package (which may need to be 17 | %% installed) using 18 | %% \usepackage{import} 19 | %% in the preamble, and then including the image with 20 | %% \import{}{.pdf_tex} 21 | %% Alternatively, one can specify 22 | %% \graphicspath{{/}} 23 | %% 24 | %% For more information, please see info/svg-inkscape on CTAN: 25 | %% http://tug.ctan.org/tex-archive/info/svg-inkscape 26 | %% 27 | \begingroup% 28 | \makeatletter% 29 | \providecommand\color[2][]{% 30 | \errmessage{(Inkscape) Color is used for the text in Inkscape, but the package 'color.sty' is not loaded}% 31 | \renewcommand\color[2][]{}% 32 | }% 33 | \providecommand\transparent[1]{% 34 | \errmessage{(Inkscape) Transparency is used (non-zero) for the text in Inkscape, but the package 'transparent.sty' is not loaded}% 35 | \renewcommand\transparent[1]{}% 36 | }% 37 | \providecommand\rotatebox[2]{#2}% 38 | \newcommand*\fsize{\dimexpr\f@size pt\relax}% 39 | \newcommand*\lineheight[1]{\fontsize{\fsize}{#1\fsize}\selectfont}% 40 | \ifx\svgwidth\undefined% 41 | \setlength{\unitlength}{327.04620602bp}% 42 | \ifx\svgscale\undefined% 43 | \relax% 44 | \else% 45 | \setlength{\unitlength}{\unitlength * \real{\svgscale}}% 46 | \fi% 47 | \else% 48 | \setlength{\unitlength}{\svgwidth}% 49 | \fi% 50 | \global\let\svgwidth\undefined% 51 | \global\let\svgscale\undefined% 52 | \makeatother% 53 | \begin{picture}(1,0.57345475)% 54 | \lineheight{1}% 55 | \setlength\tabcolsep{0pt}% 56 | \put(0,0){\includegraphics[width=\unitlength,page=1]{example-when-fp-is-not-a-morse-function.pdf}}% 57 | \put(0.57956723,0.49850814){\color[rgb]{0,0,0}\makebox(0,0)[lt]{\lineheight{1.25}\smash{\begin{tabular}[t]{l}$M = S^{1}$\end{tabular}}}}% 58 | \put(0,0){\includegraphics[width=\unitlength,page=2]{example-when-fp-is-not-a-morse-function.pdf}}% 59 | \put(0.41819981,0.31089804){\color[rgb]{0,0,0}\makebox(0,0)[lt]{\lineheight{1.25}\smash{\begin{tabular}[t]{l}$p$\end{tabular}}}}% 60 | \put(0.6732588,0.40108752){\color[rgb]{0,0,0}\makebox(0,0)[lt]{\lineheight{1.25}\smash{\begin{tabular}[t]{l}$f_p \equiv 1$\end{tabular}}}}% 61 | \put(0,0){\includegraphics[width=\unitlength,page=3]{example-when-fp-is-not-a-morse-function.pdf}}% 62 | \end{picture}% 63 | \endgroup% 64 | -------------------------------------------------------------------------------- /thesis/figures/examples-of-cobordisms.pdf: -------------------------------------------------------------------------------- https://raw.githubusercontent.com/gillescastel/masterthesis/16b33d4121a8958e624bb0c9157151a63311b119/thesis/figures/examples-of-cobordisms.pdf -------------------------------------------------------------------------------- /thesis/figures/examples-of-morse-functions.pdf: -------------------------------------------------------------------------------- https://raw.githubusercontent.com/gillescastel/masterthesis/16b33d4121a8958e624bb0c9157151a63311b119/thesis/figures/examples-of-morse-functions.pdf -------------------------------------------------------------------------------- /thesis/figures/examples-of-morse-functions.pdf_tex: -------------------------------------------------------------------------------- 1 | %% Creator: Inkscape inkscape 0.92.4, www.inkscape.org 2 | %% PDF/EPS/PS + LaTeX output extension by Johan Engelen, 2010 3 | %% Accompanies image file 'examples-of-morse-functions.pdf' (pdf, eps, ps) 4 | %% 5 | %% To include the image in your LaTeX document, write 6 | %% \input{.pdf_tex} 7 | %% instead of 8 | %% \includegraphics{.pdf} 9 | %% To scale the image, write 10 | %% \def\svgwidth{} 11 | %% \input{.pdf_tex} 12 | %% instead of 13 | %% \includegraphics[width=]{.pdf} 14 | %% 15 | %% Images with a different path to the parent latex file can 16 | %% be accessed with the `import' package (which may need to be 17 | %% installed) using 18 | %% \usepackage{import} 19 | %% in the preamble, and then including the image with 20 | %% \import{}{.pdf_tex} 21 | %% Alternatively, one can specify 22 | %% \graphicspath{{/}} 23 | %% 24 | %% For more information, please see info/svg-inkscape on CTAN: 25 | %% http://tug.ctan.org/tex-archive/info/svg-inkscape 26 | %% 27 | \begingroup% 28 | \makeatletter% 29 | \providecommand\color[2][]{% 30 | \errmessage{(Inkscape) Color is used for the text in Inkscape, but the package 'color.sty' is not loaded}% 31 | \renewcommand\color[2][]{}% 32 | }% 33 | \providecommand\transparent[1]{% 34 | \errmessage{(Inkscape) Transparency is used (non-zero) for the text in Inkscape, but the package 'transparent.sty' is not loaded}% 35 | \renewcommand\transparent[1]{}% 36 | }% 37 | \providecommand\rotatebox[2]{#2}% 38 | \newcommand*\fsize{\dimexpr\f@size pt\relax}% 39 | \newcommand*\lineheight[1]{\fontsize{\fsize}{#1\fsize}\selectfont}% 40 | \ifx\svgwidth\undefined% 41 | \setlength{\unitlength}{286.76727776bp}% 42 | \ifx\svgscale\undefined% 43 | \relax% 44 | \else% 45 | \setlength{\unitlength}{\unitlength * \real{\svgscale}}% 46 | \fi% 47 | \else% 48 | \setlength{\unitlength}{\svgwidth}% 49 | \fi% 50 | \global\let\svgwidth\undefined% 51 | \global\let\svgscale\undefined% 52 | \makeatother% 53 | \begin{picture}(1,0.70615098)% 54 | \lineheight{1}% 55 | \setlength\tabcolsep{0pt}% 56 | \put(0,0){\includegraphics[width=\unitlength,page=1]{examples-of-morse-functions.pdf}}% 57 | \put(0.82679593,0.40595397){\color[rgb]{0,0,0}\makebox(0,0)[lt]{\lineheight{1.25}\smash{\begin{tabular}[t]{l}$h$\end{tabular}}}}% 58 | \put(0,0){\includegraphics[width=\unitlength,page=2]{examples-of-morse-functions.pdf}}% 59 | \put(0.50162641,0.69746489){\color[rgb]{0,0,0}\makebox(0,0)[lt]{\lineheight{1.25}\smash{\begin{tabular}[t]{l}$k=2$\end{tabular}}}}% 60 | \put(0.49838544,0.52140418){\color[rgb]{0,0,0}\makebox(0,0)[lt]{\lineheight{1.25}\smash{\begin{tabular}[t]{l}$k=1$\end{tabular}}}}% 61 | \put(0.50029197,0.18991759){\color[rgb]{0,0,0}\makebox(0,0)[lt]{\lineheight{1.25}\smash{\begin{tabular}[t]{l}$k=1$\end{tabular}}}}% 62 | \put(0.49789548,-0.00089117){\color[rgb]{0,0,0}\makebox(0,0)[lt]{\lineheight{1.25}\smash{\begin{tabular}[t]{l}$k=0$\end{tabular}}}}% 63 | \end{picture}% 64 | \endgroup% 65 | -------------------------------------------------------------------------------- /thesis/figures/existence-of-morse-functions-normal-bundle-map.pdf: -------------------------------------------------------------------------------- https://raw.githubusercontent.com/gillescastel/masterthesis/16b33d4121a8958e624bb0c9157151a63311b119/thesis/figures/existence-of-morse-functions-normal-bundle-map.pdf -------------------------------------------------------------------------------- /thesis/figures/finding-holes-using-singular-homology.pdf: -------------------------------------------------------------------------------- https://raw.githubusercontent.com/gillescastel/masterthesis/16b33d4121a8958e624bb0c9157151a63311b119/thesis/figures/finding-holes-using-singular-homology.pdf -------------------------------------------------------------------------------- /thesis/figures/finding-holes-using-singular-homology.pdf_tex: -------------------------------------------------------------------------------- 1 | %% Creator: Inkscape inkscape 0.92.4, www.inkscape.org 2 | %% PDF/EPS/PS + LaTeX output extension by Johan Engelen, 2010 3 | %% Accompanies image file 'finding-holes-using-singular-homology.pdf' (pdf, eps, ps) 4 | %% 5 | %% To include the image in your LaTeX document, write 6 | %% \input{.pdf_tex} 7 | %% instead of 8 | %% \includegraphics{.pdf} 9 | %% To scale the image, write 10 | %% \def\svgwidth{} 11 | %% \input{.pdf_tex} 12 | %% instead of 13 | %% \includegraphics[width=]{.pdf} 14 | %% 15 | %% Images with a different path to the parent latex file can 16 | %% be accessed with the `import' package (which may need to be 17 | %% installed) using 18 | %% \usepackage{import} 19 | %% in the preamble, and then including the image with 20 | %% \import{}{.pdf_tex} 21 | %% Alternatively, one can specify 22 | %% \graphicspath{{/}} 23 | %% 24 | %% For more information, please see info/svg-inkscape on CTAN: 25 | %% http://tug.ctan.org/tex-archive/info/svg-inkscape 26 | %% 27 | \begingroup% 28 | \makeatletter% 29 | \providecommand\color[2][]{% 30 | \errmessage{(Inkscape) Color is used for the text in Inkscape, but the package 'color.sty' is not loaded}% 31 | \renewcommand\color[2][]{}% 32 | }% 33 | \providecommand\transparent[1]{% 34 | \errmessage{(Inkscape) Transparency is used (non-zero) for the text in Inkscape, but the package 'transparent.sty' is not loaded}% 35 | \renewcommand\transparent[1]{}% 36 | }% 37 | \providecommand\rotatebox[2]{#2}% 38 | \newcommand*\fsize{\dimexpr\f@size pt\relax}% 39 | \newcommand*\lineheight[1]{\fontsize{\fsize}{#1\fsize}\selectfont}% 40 | \ifx\svgwidth\undefined% 41 | \setlength{\unitlength}{224.53881211bp}% 42 | \ifx\svgscale\undefined% 43 | \relax% 44 | \else% 45 | \setlength{\unitlength}{\unitlength * \real{\svgscale}}% 46 | \fi% 47 | \else% 48 | \setlength{\unitlength}{\svgwidth}% 49 | \fi% 50 | \global\let\svgwidth\undefined% 51 | \global\let\svgscale\undefined% 52 | \makeatother% 53 | \begin{picture}(1,0.70585422)% 54 | \lineheight{1}% 55 | \setlength\tabcolsep{0pt}% 56 | \put(0,0){\includegraphics[width=\unitlength,page=1]{finding-holes-using-singular-homology.pdf}}% 57 | \put(0.61844563,0.50721646){\color[rgb]{0,0,0}\makebox(0,0)[lt]{\lineheight{1.25}\smash{\begin{tabular}[t]{l}$\sigma$\end{tabular}}}}% 58 | \put(0.25398914,0.52651371){\color[rgb]{0,0,0}\makebox(0,0)[lt]{\lineheight{1.25}\smash{\begin{tabular}[t]{l}$\rho$\end{tabular}}}}% 59 | \put(0,0){\includegraphics[width=\unitlength,page=2]{finding-holes-using-singular-homology.pdf}}% 60 | \put(0.789462,0.37657894){\color[rgb]{0,0,0}\makebox(0,0)[lt]{\lineheight{1.25}\smash{\begin{tabular}[t]{l}$\phi$\end{tabular}}}}% 61 | \end{picture}% 62 | \endgroup% 63 | -------------------------------------------------------------------------------- /thesis/figures/fundamental-group-operation.pdf: -------------------------------------------------------------------------------- https://raw.githubusercontent.com/gillescastel/masterthesis/16b33d4121a8958e624bb0c9157151a63311b119/thesis/figures/fundamental-group-operation.pdf -------------------------------------------------------------------------------- /thesis/figures/genus-four-heegaard-splitting-of-s3.pdf: -------------------------------------------------------------------------------- https://raw.githubusercontent.com/gillescastel/masterthesis/16b33d4121a8958e624bb0c9157151a63311b119/thesis/figures/genus-four-heegaard-splitting-of-s3.pdf -------------------------------------------------------------------------------- /thesis/figures/genus-four-heegaard-splitting-of-s3.pdf_tex: -------------------------------------------------------------------------------- 1 | %% Creator: Inkscape inkscape 0.92.4, www.inkscape.org 2 | %% PDF/EPS/PS + LaTeX output extension by Johan Engelen, 2010 3 | %% Accompanies image file 'genus-four-heegaard-splitting-of-s3.pdf' (pdf, eps, ps) 4 | %% 5 | %% To include the image in your LaTeX document, write 6 | %% \input{.pdf_tex} 7 | %% instead of 8 | %% \includegraphics{.pdf} 9 | %% To scale the image, write 10 | %% \def\svgwidth{} 11 | %% \input{.pdf_tex} 12 | %% instead of 13 | %% \includegraphics[width=]{.pdf} 14 | %% 15 | %% Images with a different path to the parent latex file can 16 | %% be accessed with the `import' package (which may need to be 17 | %% installed) using 18 | %% \usepackage{import} 19 | %% in the preamble, and then including the image with 20 | %% \import{}{.pdf_tex} 21 | %% Alternatively, one can specify 22 | %% \graphicspath{{/}} 23 | %% 24 | %% For more information, please see info/svg-inkscape on CTAN: 25 | %% http://tug.ctan.org/tex-archive/info/svg-inkscape 26 | %% 27 | \begingroup% 28 | \makeatletter% 29 | \providecommand\color[2][]{% 30 | \errmessage{(Inkscape) Color is used for the text in Inkscape, but the package 'color.sty' is not loaded}% 31 | \renewcommand\color[2][]{}% 32 | }% 33 | \providecommand\transparent[1]{% 34 | \errmessage{(Inkscape) Transparency is used (non-zero) for the text in Inkscape, but the package 'transparent.sty' is not loaded}% 35 | \renewcommand\transparent[1]{}% 36 | }% 37 | \providecommand\rotatebox[2]{#2}% 38 | \newcommand*\fsize{\dimexpr\f@size pt\relax}% 39 | \newcommand*\lineheight[1]{\fontsize{\fsize}{#1\fsize}\selectfont}% 40 | \ifx\svgwidth\undefined% 41 | \setlength{\unitlength}{191.03286863bp}% 42 | \ifx\svgscale\undefined% 43 | \relax% 44 | \else% 45 | \setlength{\unitlength}{\unitlength * \real{\svgscale}}% 46 | \fi% 47 | \else% 48 | \setlength{\unitlength}{\svgwidth}% 49 | \fi% 50 | \global\let\svgwidth\undefined% 51 | \global\let\svgscale\undefined% 52 | \makeatother% 53 | \begin{picture}(1,0.45357703)% 54 | \lineheight{1}% 55 | \setlength\tabcolsep{0pt}% 56 | \put(0,0){\includegraphics[width=\unitlength,page=1]{genus-four-heegaard-splitting-of-s3.pdf}}% 57 | \end{picture}% 58 | \endgroup% 59 | -------------------------------------------------------------------------------- /thesis/figures/handle-1-0.pdf: -------------------------------------------------------------------------------- https://raw.githubusercontent.com/gillescastel/masterthesis/16b33d4121a8958e624bb0c9157151a63311b119/thesis/figures/handle-1-0.pdf -------------------------------------------------------------------------------- /thesis/figures/handle-1-0.pdf_tex: -------------------------------------------------------------------------------- 1 | %% Creator: Inkscape inkscape 0.92.4, www.inkscape.org 2 | %% PDF/EPS/PS + LaTeX output extension by Johan Engelen, 2010 3 | %% Accompanies image file 'handle-1-0.pdf' (pdf, eps, ps) 4 | %% 5 | %% To include the image in your LaTeX document, write 6 | %% \input{.pdf_tex} 7 | %% instead of 8 | %% \includegraphics{.pdf} 9 | %% To scale the image, write 10 | %% \def\svgwidth{} 11 | %% \input{.pdf_tex} 12 | %% instead of 13 | %% \includegraphics[width=]{.pdf} 14 | %% 15 | %% Images with a different path to the parent latex file can 16 | %% be accessed with the `import' package (which may need to be 17 | %% installed) using 18 | %% \usepackage{import} 19 | %% in the preamble, and then including the image with 20 | %% \import{}{.pdf_tex} 21 | %% Alternatively, one can specify 22 | %% \graphicspath{{/}} 23 | %% 24 | %% For more information, please see info/svg-inkscape on CTAN: 25 | %% http://tug.ctan.org/tex-archive/info/svg-inkscape 26 | %% 27 | \begingroup% 28 | \makeatletter% 29 | \providecommand\color[2][]{% 30 | \errmessage{(Inkscape) Color is used for the text in Inkscape, but the package 'color.sty' is not loaded}% 31 | \renewcommand\color[2][]{}% 32 | }% 33 | \providecommand\transparent[1]{% 34 | \errmessage{(Inkscape) Transparency is used (non-zero) for the text in Inkscape, but the package 'transparent.sty' is not loaded}% 35 | \renewcommand\transparent[1]{}% 36 | }% 37 | \providecommand\rotatebox[2]{#2}% 38 | \newcommand*\fsize{\dimexpr\f@size pt\relax}% 39 | \newcommand*\lineheight[1]{\fontsize{\fsize}{#1\fsize}\selectfont}% 40 | \ifx\svgwidth\undefined% 41 | \setlength{\unitlength}{23.04432876bp}% 42 | \ifx\svgscale\undefined% 43 | \relax% 44 | \else% 45 | \setlength{\unitlength}{\unitlength * \real{\svgscale}}% 46 | \fi% 47 | \else% 48 | \setlength{\unitlength}{\svgwidth}% 49 | \fi% 50 | \global\let\svgwidth\undefined% 51 | \global\let\svgscale\undefined% 52 | \makeatother% 53 | \begin{picture}(1,0.49693581)% 54 | \lineheight{1}% 55 | \setlength\tabcolsep{0pt}% 56 | \put(0,0){\includegraphics[width=\unitlength,page=1]{handle-1-0.pdf}}% 57 | \end{picture}% 58 | \endgroup% 59 | -------------------------------------------------------------------------------- /thesis/figures/handle-1-0.svg: -------------------------------------------------------------------------------- 1 | 2 | 3 | 4 | 19 | 21 | 43 | 53 | 54 | 56 | 57 | 59 | image/svg+xml 60 | 62 | 63 | 64 | 65 | 66 | 71 | 84 | 85 | 86 | -------------------------------------------------------------------------------- /thesis/figures/handle-1-1.pdf: -------------------------------------------------------------------------------- https://raw.githubusercontent.com/gillescastel/masterthesis/16b33d4121a8958e624bb0c9157151a63311b119/thesis/figures/handle-1-1.pdf -------------------------------------------------------------------------------- /thesis/figures/handle-1-1.pdf_tex: -------------------------------------------------------------------------------- 1 | %% Creator: Inkscape inkscape 0.92.4, www.inkscape.org 2 | %% PDF/EPS/PS + LaTeX output extension by Johan Engelen, 2010 3 | %% Accompanies image file 'handle-1-1.pdf' (pdf, eps, ps) 4 | %% 5 | %% To include the image in your LaTeX document, write 6 | %% \input{.pdf_tex} 7 | %% instead of 8 | %% \includegraphics{.pdf} 9 | %% To scale the image, write 10 | %% \def\svgwidth{} 11 | %% \input{.pdf_tex} 12 | %% instead of 13 | %% \includegraphics[width=]{.pdf} 14 | %% 15 | %% Images with a different path to the parent latex file can 16 | %% be accessed with the `import' package (which may need to be 17 | %% installed) using 18 | %% \usepackage{import} 19 | %% in the preamble, and then including the image with 20 | %% \import{}{.pdf_tex} 21 | %% Alternatively, one can specify 22 | %% \graphicspath{{/}} 23 | %% 24 | %% For more information, please see info/svg-inkscape on CTAN: 25 | %% http://tug.ctan.org/tex-archive/info/svg-inkscape 26 | %% 27 | \begingroup% 28 | \makeatletter% 29 | \providecommand\color[2][]{% 30 | \errmessage{(Inkscape) Color is used for the text in Inkscape, but the package 'color.sty' is not loaded}% 31 | \renewcommand\color[2][]{}% 32 | }% 33 | \providecommand\transparent[1]{% 34 | \errmessage{(Inkscape) Transparency is used (non-zero) for the text in Inkscape, but the package 'transparent.sty' is not loaded}% 35 | \renewcommand\transparent[1]{}% 36 | }% 37 | \providecommand\rotatebox[2]{#2}% 38 | \newcommand*\fsize{\dimexpr\f@size pt\relax}% 39 | \newcommand*\lineheight[1]{\fontsize{\fsize}{#1\fsize}\selectfont}% 40 | \ifx\svgwidth\undefined% 41 | \setlength{\unitlength}{25.48087413bp}% 42 | \ifx\svgscale\undefined% 43 | \relax% 44 | \else% 45 | \setlength{\unitlength}{\unitlength * \real{\svgscale}}% 46 | \fi% 47 | \else% 48 | \setlength{\unitlength}{\svgwidth}% 49 | \fi% 50 | \global\let\svgwidth\undefined% 51 | \global\let\svgscale\undefined% 52 | \makeatother% 53 | \begin{picture}(1,0.50504056)% 54 | \lineheight{1}% 55 | \setlength\tabcolsep{0pt}% 56 | \put(0,0){\includegraphics[width=\unitlength,page=1]{handle-1-1.pdf}}% 57 | \end{picture}% 58 | \endgroup% 59 | -------------------------------------------------------------------------------- /thesis/figures/handle-2-0.pdf: -------------------------------------------------------------------------------- https://raw.githubusercontent.com/gillescastel/masterthesis/16b33d4121a8958e624bb0c9157151a63311b119/thesis/figures/handle-2-0.pdf -------------------------------------------------------------------------------- /thesis/figures/handle-2-0.pdf_tex: -------------------------------------------------------------------------------- 1 | %% Creator: Inkscape inkscape 0.92.4, www.inkscape.org 2 | %% PDF/EPS/PS + LaTeX output extension by Johan Engelen, 2010 3 | %% Accompanies image file 'handle-2-0.pdf' (pdf, eps, ps) 4 | %% 5 | %% To include the image in your LaTeX document, write 6 | %% \input{.pdf_tex} 7 | %% instead of 8 | %% \includegraphics{.pdf} 9 | %% To scale the image, write 10 | %% \def\svgwidth{} 11 | %% \input{.pdf_tex} 12 | %% instead of 13 | %% \includegraphics[width=]{.pdf} 14 | %% 15 | %% Images with a different path to the parent latex file can 16 | %% be accessed with the `import' package (which may need to be 17 | %% installed) using 18 | %% \usepackage{import} 19 | %% in the preamble, and then including the image with 20 | %% \import{}{.pdf_tex} 21 | %% Alternatively, one can specify 22 | %% \graphicspath{{/}} 23 | %% 24 | %% For more information, please see info/svg-inkscape on CTAN: 25 | %% http://tug.ctan.org/tex-archive/info/svg-inkscape 26 | %% 27 | \begingroup% 28 | \makeatletter% 29 | \providecommand\color[2][]{% 30 | \errmessage{(Inkscape) Color is used for the text in Inkscape, but the package 'color.sty' is not loaded}% 31 | \renewcommand\color[2][]{}% 32 | }% 33 | \providecommand\transparent[1]{% 34 | \errmessage{(Inkscape) Transparency is used (non-zero) for the text in Inkscape, but the package 'transparent.sty' is not loaded}% 35 | \renewcommand\transparent[1]{}% 36 | }% 37 | \providecommand\rotatebox[2]{#2}% 38 | \newcommand*\fsize{\dimexpr\f@size pt\relax}% 39 | \newcommand*\lineheight[1]{\fontsize{\fsize}{#1\fsize}\selectfont}% 40 | \ifx\svgwidth\undefined% 41 | \setlength{\unitlength}{61.86636016bp}% 42 | \ifx\svgscale\undefined% 43 | \relax% 44 | \else% 45 | \setlength{\unitlength}{\unitlength * \real{\svgscale}}% 46 | \fi% 47 | \else% 48 | \setlength{\unitlength}{\svgwidth}% 49 | \fi% 50 | \global\let\svgwidth\undefined% 51 | \global\let\svgscale\undefined% 52 | \makeatother% 53 | \begin{picture}(1,1)% 54 | \lineheight{1}% 55 | \setlength\tabcolsep{0pt}% 56 | \put(0,0){\includegraphics[width=\unitlength,page=1]{handle-2-0.pdf}}% 57 | \end{picture}% 58 | \endgroup% 59 | -------------------------------------------------------------------------------- /thesis/figures/handle-2-0.svg: -------------------------------------------------------------------------------- 1 | 2 | 3 | 4 | 19 | 21 | 43 | 53 | 54 | 56 | 57 | 59 | image/svg+xml 60 | 62 | 63 | 64 | 65 | 66 | 71 | 77 | 78 | 79 | -------------------------------------------------------------------------------- /thesis/figures/handle-2-1.pdf: -------------------------------------------------------------------------------- https://raw.githubusercontent.com/gillescastel/masterthesis/16b33d4121a8958e624bb0c9157151a63311b119/thesis/figures/handle-2-1.pdf -------------------------------------------------------------------------------- /thesis/figures/handle-2-1.pdf_tex: -------------------------------------------------------------------------------- 1 | %% Creator: Inkscape inkscape 0.92.4, www.inkscape.org 2 | %% PDF/EPS/PS + LaTeX output extension by Johan Engelen, 2010 3 | %% Accompanies image file 'handle-2-1.pdf' (pdf, eps, ps) 4 | %% 5 | %% To include the image in your LaTeX document, write 6 | %% \input{.pdf_tex} 7 | %% instead of 8 | %% \includegraphics{.pdf} 9 | %% To scale the image, write 10 | %% \def\svgwidth{} 11 | %% \input{.pdf_tex} 12 | %% instead of 13 | %% \includegraphics[width=]{.pdf} 14 | %% 15 | %% Images with a different path to the parent latex file can 16 | %% be accessed with the `import' package (which may need to be 17 | %% installed) using 18 | %% \usepackage{import} 19 | %% in the preamble, and then including the image with 20 | %% \import{}{.pdf_tex} 21 | %% Alternatively, one can specify 22 | %% \graphicspath{{/}} 23 | %% 24 | %% For more information, please see info/svg-inkscape on CTAN: 25 | %% http://tug.ctan.org/tex-archive/info/svg-inkscape 26 | %% 27 | \begingroup% 28 | \makeatletter% 29 | \providecommand\color[2][]{% 30 | \errmessage{(Inkscape) Color is used for the text in Inkscape, but the package 'color.sty' is not loaded}% 31 | \renewcommand\color[2][]{}% 32 | }% 33 | \providecommand\transparent[1]{% 34 | \errmessage{(Inkscape) Transparency is used (non-zero) for the text in Inkscape, but the package 'transparent.sty' is not loaded}% 35 | \renewcommand\transparent[1]{}% 36 | }% 37 | \providecommand\rotatebox[2]{#2}% 38 | \newcommand*\fsize{\dimexpr\f@size pt\relax}% 39 | \newcommand*\lineheight[1]{\fontsize{\fsize}{#1\fsize}\selectfont}% 40 | \ifx\svgwidth\undefined% 41 | \setlength{\unitlength}{40.85833542bp}% 42 | \ifx\svgscale\undefined% 43 | \relax% 44 | \else% 45 | \setlength{\unitlength}{\unitlength * \real{\svgscale}}% 46 | \fi% 47 | \else% 48 | \setlength{\unitlength}{\svgwidth}% 49 | \fi% 50 | \global\let\svgwidth\undefined% 51 | \global\let\svgscale\undefined% 52 | \makeatother% 53 | \begin{picture}(1,0.31243215)% 54 | \lineheight{1}% 55 | \setlength\tabcolsep{0pt}% 56 | \put(0,0){\includegraphics[width=\unitlength,page=1]{handle-2-1.pdf}}% 57 | \end{picture}% 58 | \endgroup% 59 | -------------------------------------------------------------------------------- /thesis/figures/handle-2-2.pdf: -------------------------------------------------------------------------------- https://raw.githubusercontent.com/gillescastel/masterthesis/16b33d4121a8958e624bb0c9157151a63311b119/thesis/figures/handle-2-2.pdf -------------------------------------------------------------------------------- /thesis/figures/handle-2-2.pdf_tex: -------------------------------------------------------------------------------- 1 | %% Creator: Inkscape inkscape 0.92.4, www.inkscape.org 2 | %% PDF/EPS/PS + LaTeX output extension by Johan Engelen, 2010 3 | %% Accompanies image file 'handle-2-2.pdf' (pdf, eps, ps) 4 | %% 5 | %% To include the image in your LaTeX document, write 6 | %% \input{.pdf_tex} 7 | %% instead of 8 | %% \includegraphics{.pdf} 9 | %% To scale the image, write 10 | %% \def\svgwidth{} 11 | %% \input{.pdf_tex} 12 | %% instead of 13 | %% \includegraphics[width=]{.pdf} 14 | %% 15 | %% Images with a different path to the parent latex file can 16 | %% be accessed with the `import' package (which may need to be 17 | %% installed) using 18 | %% \usepackage{import} 19 | %% in the preamble, and then including the image with 20 | %% \import{}{.pdf_tex} 21 | %% Alternatively, one can specify 22 | %% \graphicspath{{/}} 23 | %% 24 | %% For more information, please see info/svg-inkscape on CTAN: 25 | %% http://tug.ctan.org/tex-archive/info/svg-inkscape 26 | %% 27 | \begingroup% 28 | \makeatletter% 29 | \providecommand\color[2][]{% 30 | \errmessage{(Inkscape) Color is used for the text in Inkscape, but the package 'color.sty' is not loaded}% 31 | \renewcommand\color[2][]{}% 32 | }% 33 | \providecommand\transparent[1]{% 34 | \errmessage{(Inkscape) Transparency is used (non-zero) for the text in Inkscape, but the package 'transparent.sty' is not loaded}% 35 | \renewcommand\transparent[1]{}% 36 | }% 37 | \providecommand\rotatebox[2]{#2}% 38 | \newcommand*\fsize{\dimexpr\f@size pt\relax}% 39 | \newcommand*\lineheight[1]{\fontsize{\fsize}{#1\fsize}\selectfont}% 40 | \ifx\svgwidth\undefined% 41 | \setlength{\unitlength}{45.99407887bp}% 42 | \ifx\svgscale\undefined% 43 | \relax% 44 | \else% 45 | \setlength{\unitlength}{\unitlength * \real{\svgscale}}% 46 | \fi% 47 | \else% 48 | \setlength{\unitlength}{\svgwidth}% 49 | \fi% 50 | \global\let\svgwidth\undefined% 51 | \global\let\svgscale\undefined% 52 | \makeatother% 53 | \begin{picture}(1,1)% 54 | \lineheight{1}% 55 | \setlength\tabcolsep{0pt}% 56 | \put(0,0){\includegraphics[width=\unitlength,page=1]{handle-2-2.pdf}}% 57 | \end{picture}% 58 | \endgroup% 59 | -------------------------------------------------------------------------------- /thesis/figures/handle-2-2.svg: -------------------------------------------------------------------------------- 1 | 2 | 3 | 4 | 19 | 21 | 43 | 53 | 54 | 56 | 57 | 59 | image/svg+xml 60 | 62 | 63 | 64 | 65 | 66 | 71 | 77 | 78 | 79 | -------------------------------------------------------------------------------- /thesis/figures/handle-3-0.pdf: -------------------------------------------------------------------------------- https://raw.githubusercontent.com/gillescastel/masterthesis/16b33d4121a8958e624bb0c9157151a63311b119/thesis/figures/handle-3-0.pdf -------------------------------------------------------------------------------- /thesis/figures/handle-3-0.pdf_tex: -------------------------------------------------------------------------------- 1 | %% Creator: Inkscape inkscape 0.92.4, www.inkscape.org 2 | %% PDF/EPS/PS + LaTeX output extension by Johan Engelen, 2010 3 | %% Accompanies image file 'handle-3-0.pdf' (pdf, eps, ps) 4 | %% 5 | %% To include the image in your LaTeX document, write 6 | %% \input{.pdf_tex} 7 | %% instead of 8 | %% \includegraphics{.pdf} 9 | %% To scale the image, write 10 | %% \def\svgwidth{} 11 | %% \input{.pdf_tex} 12 | %% instead of 13 | %% \includegraphics[width=]{.pdf} 14 | %% 15 | %% Images with a different path to the parent latex file can 16 | %% be accessed with the `import' package (which may need to be 17 | %% installed) using 18 | %% \usepackage{import} 19 | %% in the preamble, and then including the image with 20 | %% \import{}{.pdf_tex} 21 | %% Alternatively, one can specify 22 | %% \graphicspath{{/}} 23 | %% 24 | %% For more information, please see info/svg-inkscape on CTAN: 25 | %% http://tug.ctan.org/tex-archive/info/svg-inkscape 26 | %% 27 | \begingroup% 28 | \makeatletter% 29 | \providecommand\color[2][]{% 30 | \errmessage{(Inkscape) Color is used for the text in Inkscape, but the package 'color.sty' is not loaded}% 31 | \renewcommand\color[2][]{}% 32 | }% 33 | \providecommand\transparent[1]{% 34 | \errmessage{(Inkscape) Transparency is used (non-zero) for the text in Inkscape, but the package 'transparent.sty' is not loaded}% 35 | \renewcommand\transparent[1]{}% 36 | }% 37 | \providecommand\rotatebox[2]{#2}% 38 | \newcommand*\fsize{\dimexpr\f@size pt\relax}% 39 | \newcommand*\lineheight[1]{\fontsize{\fsize}{#1\fsize}\selectfont}% 40 | \ifx\svgwidth\undefined% 41 | \setlength{\unitlength}{62.26445776bp}% 42 | \ifx\svgscale\undefined% 43 | \relax% 44 | \else% 45 | \setlength{\unitlength}{\unitlength * \real{\svgscale}}% 46 | \fi% 47 | \else% 48 | \setlength{\unitlength}{\svgwidth}% 49 | \fi% 50 | \global\let\svgwidth\undefined% 51 | \global\let\svgscale\undefined% 52 | \makeatother% 53 | \begin{picture}(1,1)% 54 | \lineheight{1}% 55 | \setlength\tabcolsep{0pt}% 56 | \put(0,0){\includegraphics[width=\unitlength,page=1]{handle-3-0.pdf}}% 57 | \end{picture}% 58 | \endgroup% 59 | -------------------------------------------------------------------------------- /thesis/figures/handle-3-1.pdf: -------------------------------------------------------------------------------- https://raw.githubusercontent.com/gillescastel/masterthesis/16b33d4121a8958e624bb0c9157151a63311b119/thesis/figures/handle-3-1.pdf -------------------------------------------------------------------------------- /thesis/figures/handle-3-1.pdf_tex: -------------------------------------------------------------------------------- 1 | %% Creator: Inkscape inkscape 0.92.4, www.inkscape.org 2 | %% PDF/EPS/PS + LaTeX output extension by Johan Engelen, 2010 3 | %% Accompanies image file 'handle-3-1.pdf' (pdf, eps, ps) 4 | %% 5 | %% To include the image in your LaTeX document, write 6 | %% \input{.pdf_tex} 7 | %% instead of 8 | %% \includegraphics{.pdf} 9 | %% To scale the image, write 10 | %% \def\svgwidth{} 11 | %% \input{.pdf_tex} 12 | %% instead of 13 | %% \includegraphics[width=]{.pdf} 14 | %% 15 | %% Images with a different path to the parent latex file can 16 | %% be accessed with the `import' package (which may need to be 17 | %% installed) using 18 | %% \usepackage{import} 19 | %% in the preamble, and then including the image with 20 | %% \import{}{.pdf_tex} 21 | %% Alternatively, one can specify 22 | %% \graphicspath{{/}} 23 | %% 24 | %% For more information, please see info/svg-inkscape on CTAN: 25 | %% http://tug.ctan.org/tex-archive/info/svg-inkscape 26 | %% 27 | \begingroup% 28 | \makeatletter% 29 | \providecommand\color[2][]{% 30 | \errmessage{(Inkscape) Color is used for the text in Inkscape, but the package 'color.sty' is not loaded}% 31 | \renewcommand\color[2][]{}% 32 | }% 33 | \providecommand\transparent[1]{% 34 | \errmessage{(Inkscape) Transparency is used (non-zero) for the text in Inkscape, but the package 'transparent.sty' is not loaded}% 35 | \renewcommand\transparent[1]{}% 36 | }% 37 | \providecommand\rotatebox[2]{#2}% 38 | \newcommand*\fsize{\dimexpr\f@size pt\relax}% 39 | \newcommand*\lineheight[1]{\fontsize{\fsize}{#1\fsize}\selectfont}% 40 | \ifx\svgwidth\undefined% 41 | \setlength{\unitlength}{76.64187394bp}% 42 | \ifx\svgscale\undefined% 43 | \relax% 44 | \else% 45 | \setlength{\unitlength}{\unitlength * \real{\svgscale}}% 46 | \fi% 47 | \else% 48 | \setlength{\unitlength}{\svgwidth}% 49 | \fi% 50 | \global\let\svgwidth\undefined% 51 | \global\let\svgscale\undefined% 52 | \makeatother% 53 | \begin{picture}(1,0.73550388)% 54 | \lineheight{1}% 55 | \setlength\tabcolsep{0pt}% 56 | \put(0,0){\includegraphics[width=\unitlength,page=1]{handle-3-1.pdf}}% 57 | \end{picture}% 58 | \endgroup% 59 | -------------------------------------------------------------------------------- /thesis/figures/handle-3-2.pdf: -------------------------------------------------------------------------------- https://raw.githubusercontent.com/gillescastel/masterthesis/16b33d4121a8958e624bb0c9157151a63311b119/thesis/figures/handle-3-2.pdf -------------------------------------------------------------------------------- /thesis/figures/handle-3-2.pdf_tex: -------------------------------------------------------------------------------- 1 | %% Creator: Inkscape inkscape 0.92.4, www.inkscape.org 2 | %% PDF/EPS/PS + LaTeX output extension by Johan Engelen, 2010 3 | %% Accompanies image file 'handle-3-2.pdf' (pdf, eps, ps) 4 | %% 5 | %% To include the image in your LaTeX document, write 6 | %% \input{.pdf_tex} 7 | %% instead of 8 | %% \includegraphics{.pdf} 9 | %% To scale the image, write 10 | %% \def\svgwidth{} 11 | %% \input{.pdf_tex} 12 | %% instead of 13 | %% \includegraphics[width=]{.pdf} 14 | %% 15 | %% Images with a different path to the parent latex file can 16 | %% be accessed with the `import' package (which may need to be 17 | %% installed) using 18 | %% \usepackage{import} 19 | %% in the preamble, and then including the image with 20 | %% \import{}{.pdf_tex} 21 | %% Alternatively, one can specify 22 | %% \graphicspath{{/}} 23 | %% 24 | %% For more information, please see info/svg-inkscape on CTAN: 25 | %% http://tug.ctan.org/tex-archive/info/svg-inkscape 26 | %% 27 | \begingroup% 28 | \makeatletter% 29 | \providecommand\color[2][]{% 30 | \errmessage{(Inkscape) Color is used for the text in Inkscape, but the package 'color.sty' is not loaded}% 31 | \renewcommand\color[2][]{}% 32 | }% 33 | \providecommand\transparent[1]{% 34 | \errmessage{(Inkscape) Transparency is used (non-zero) for the text in Inkscape, but the package 'transparent.sty' is not loaded}% 35 | \renewcommand\transparent[1]{}% 36 | }% 37 | \providecommand\rotatebox[2]{#2}% 38 | \newcommand*\fsize{\dimexpr\f@size pt\relax}% 39 | \newcommand*\lineheight[1]{\fontsize{\fsize}{#1\fsize}\selectfont}% 40 | \ifx\svgwidth\undefined% 41 | \setlength{\unitlength}{37.1736929bp}% 42 | \ifx\svgscale\undefined% 43 | \relax% 44 | \else% 45 | \setlength{\unitlength}{\unitlength * \real{\svgscale}}% 46 | \fi% 47 | \else% 48 | \setlength{\unitlength}{\svgwidth}% 49 | \fi% 50 | \global\let\svgwidth\undefined% 51 | \global\let\svgscale\undefined% 52 | \makeatother% 53 | \begin{picture}(1,0.77319289)% 54 | \lineheight{1}% 55 | \setlength\tabcolsep{0pt}% 56 | \put(0,0){\includegraphics[width=\unitlength,page=1]{handle-3-2.pdf}}% 57 | \end{picture}% 58 | \endgroup% 59 | -------------------------------------------------------------------------------- /thesis/figures/handle-3-3.pdf: -------------------------------------------------------------------------------- https://raw.githubusercontent.com/gillescastel/masterthesis/16b33d4121a8958e624bb0c9157151a63311b119/thesis/figures/handle-3-3.pdf -------------------------------------------------------------------------------- /thesis/figures/handle-3-3.pdf_tex: -------------------------------------------------------------------------------- 1 | %% Creator: Inkscape inkscape 0.92.4, www.inkscape.org 2 | %% PDF/EPS/PS + LaTeX output extension by Johan Engelen, 2010 3 | %% Accompanies image file 'handle-3-3.pdf' (pdf, eps, ps) 4 | %% 5 | %% To include the image in your LaTeX document, write 6 | %% \input{.pdf_tex} 7 | %% instead of 8 | %% \includegraphics{.pdf} 9 | %% To scale the image, write 10 | %% \def\svgwidth{} 11 | %% \input{.pdf_tex} 12 | %% instead of 13 | %% \includegraphics[width=]{.pdf} 14 | %% 15 | %% Images with a different path to the parent latex file can 16 | %% be accessed with the `import' package (which may need to be 17 | %% installed) using 18 | %% \usepackage{import} 19 | %% in the preamble, and then including the image with 20 | %% \import{}{.pdf_tex} 21 | %% Alternatively, one can specify 22 | %% \graphicspath{{/}} 23 | %% 24 | %% For more information, please see info/svg-inkscape on CTAN: 25 | %% http://tug.ctan.org/tex-archive/info/svg-inkscape 26 | %% 27 | \begingroup% 28 | \makeatletter% 29 | \providecommand\color[2][]{% 30 | \errmessage{(Inkscape) Color is used for the text in Inkscape, but the package 'color.sty' is not loaded}% 31 | \renewcommand\color[2][]{}% 32 | }% 33 | \providecommand\transparent[1]{% 34 | \errmessage{(Inkscape) Transparency is used (non-zero) for the text in Inkscape, but the package 'transparent.sty' is not loaded}% 35 | \renewcommand\transparent[1]{}% 36 | }% 37 | \providecommand\rotatebox[2]{#2}% 38 | \newcommand*\fsize{\dimexpr\f@size pt\relax}% 39 | \newcommand*\lineheight[1]{\fontsize{\fsize}{#1\fsize}\selectfont}% 40 | \ifx\svgwidth\undefined% 41 | \setlength{\unitlength}{62.26445776bp}% 42 | \ifx\svgscale\undefined% 43 | \relax% 44 | \else% 45 | \setlength{\unitlength}{\unitlength * \real{\svgscale}}% 46 | \fi% 47 | \else% 48 | \setlength{\unitlength}{\svgwidth}% 49 | \fi% 50 | \global\let\svgwidth\undefined% 51 | \global\let\svgscale\undefined% 52 | \makeatother% 53 | \begin{picture}(1,0.99360634)% 54 | \lineheight{1}% 55 | \setlength\tabcolsep{0pt}% 56 | \put(0,0){\includegraphics[width=\unitlength,page=1]{handle-3-3.pdf}}% 57 | \end{picture}% 58 | \endgroup% 59 | -------------------------------------------------------------------------------- /thesis/figures/handle-diffeo-homeo-homotopy-equivalent.pdf: -------------------------------------------------------------------------------- https://raw.githubusercontent.com/gillescastel/masterthesis/16b33d4121a8958e624bb0c9157151a63311b119/thesis/figures/handle-diffeo-homeo-homotopy-equivalent.pdf -------------------------------------------------------------------------------- /thesis/figures/handles-in-dimension-three-s1-x-s2.pdf: -------------------------------------------------------------------------------- https://raw.githubusercontent.com/gillescastel/masterthesis/16b33d4121a8958e624bb0c9157151a63311b119/thesis/figures/handles-in-dimension-three-s1-x-s2.pdf -------------------------------------------------------------------------------- /thesis/figures/handles-in-dimension-three-s1-x-s2.pdf_tex: -------------------------------------------------------------------------------- 1 | %% Creator: Inkscape inkscape 0.92.4, www.inkscape.org 2 | %% PDF/EPS/PS + LaTeX output extension by Johan Engelen, 2010 3 | %% Accompanies image file 'handles-in-dimension-three-s1-x-s2.pdf' (pdf, eps, ps) 4 | %% 5 | %% To include the image in your LaTeX document, write 6 | %% \input{.pdf_tex} 7 | %% instead of 8 | %% \includegraphics{.pdf} 9 | %% To scale the image, write 10 | %% \def\svgwidth{} 11 | %% \input{.pdf_tex} 12 | %% instead of 13 | %% \includegraphics[width=]{.pdf} 14 | %% 15 | %% Images with a different path to the parent latex file can 16 | %% be accessed with the `import' package (which may need to be 17 | %% installed) using 18 | %% \usepackage{import} 19 | %% in the preamble, and then including the image with 20 | %% \import{}{.pdf_tex} 21 | %% Alternatively, one can specify 22 | %% \graphicspath{{/}} 23 | %% 24 | %% For more information, please see info/svg-inkscape on CTAN: 25 | %% http://tug.ctan.org/tex-archive/info/svg-inkscape 26 | %% 27 | \begingroup% 28 | \makeatletter% 29 | \providecommand\color[2][]{% 30 | \errmessage{(Inkscape) Color is used for the text in Inkscape, but the package 'color.sty' is not loaded}% 31 | \renewcommand\color[2][]{}% 32 | }% 33 | \providecommand\transparent[1]{% 34 | \errmessage{(Inkscape) Transparency is used (non-zero) for the text in Inkscape, but the package 'transparent.sty' is not loaded}% 35 | \renewcommand\transparent[1]{}% 36 | }% 37 | \providecommand\rotatebox[2]{#2}% 38 | \newcommand*\fsize{\dimexpr\f@size pt\relax}% 39 | \newcommand*\lineheight[1]{\fontsize{\fsize}{#1\fsize}\selectfont}% 40 | \ifx\svgwidth\undefined% 41 | \setlength{\unitlength}{266.27001184bp}% 42 | \ifx\svgscale\undefined% 43 | \relax% 44 | \else% 45 | \setlength{\unitlength}{\unitlength * \real{\svgscale}}% 46 | \fi% 47 | \else% 48 | \setlength{\unitlength}{\svgwidth}% 49 | \fi% 50 | \global\let\svgwidth\undefined% 51 | \global\let\svgscale\undefined% 52 | \makeatother% 53 | \begin{picture}(1,1.131667)% 54 | \lineheight{1}% 55 | \setlength\tabcolsep{0pt}% 56 | \put(0,0){\includegraphics[width=\unitlength,page=1]{handles-in-dimension-three-s1-x-s2.pdf}}% 57 | \put(0.7000454,1.07632864){\color[rgb]{0,0,0}\makebox(0,0)[lt]{\lineheight{1.25}\smash{\begin{tabular}[t]{l}$\cup $ $3$-handle\end{tabular}}}}% 58 | \put(0.7000454,0.46529445){\color[rgb]{0,0,0}\makebox(0,0)[lt]{\lineheight{1.25}\smash{\begin{tabular}[t]{l}$\cup $ $3$-handle\end{tabular}}}}% 59 | \put(0,0){\includegraphics[width=\unitlength,page=2]{handles-in-dimension-three-s1-x-s2.pdf}}% 60 | \end{picture}% 61 | \endgroup% 62 | -------------------------------------------------------------------------------- /thesis/figures/handles-in-dimension-two-other-sphere.pdf: -------------------------------------------------------------------------------- https://raw.githubusercontent.com/gillescastel/masterthesis/16b33d4121a8958e624bb0c9157151a63311b119/thesis/figures/handles-in-dimension-two-other-sphere.pdf -------------------------------------------------------------------------------- /thesis/figures/handles-in-dimension-two-other-sphere.pdf_tex: -------------------------------------------------------------------------------- 1 | %% Creator: Inkscape inkscape 0.92.4, www.inkscape.org 2 | %% PDF/EPS/PS + LaTeX output extension by Johan Engelen, 2010 3 | %% Accompanies image file 'handles-in-dimension-two-other-sphere.pdf' (pdf, eps, ps) 4 | %% 5 | %% To include the image in your LaTeX document, write 6 | %% \input{.pdf_tex} 7 | %% instead of 8 | %% \includegraphics{.pdf} 9 | %% To scale the image, write 10 | %% \def\svgwidth{} 11 | %% \input{.pdf_tex} 12 | %% instead of 13 | %% \includegraphics[width=]{.pdf} 14 | %% 15 | %% Images with a different path to the parent latex file can 16 | %% be accessed with the `import' package (which may need to be 17 | %% installed) using 18 | %% \usepackage{import} 19 | %% in the preamble, and then including the image with 20 | %% \import{}{.pdf_tex} 21 | %% Alternatively, one can specify 22 | %% \graphicspath{{/}} 23 | %% 24 | %% For more information, please see info/svg-inkscape on CTAN: 25 | %% http://tug.ctan.org/tex-archive/info/svg-inkscape 26 | %% 27 | \begingroup% 28 | \makeatletter% 29 | \providecommand\color[2][]{% 30 | \errmessage{(Inkscape) Color is used for the text in Inkscape, but the package 'color.sty' is not loaded}% 31 | \renewcommand\color[2][]{}% 32 | }% 33 | \providecommand\transparent[1]{% 34 | \errmessage{(Inkscape) Transparency is used (non-zero) for the text in Inkscape, but the package 'transparent.sty' is not loaded}% 35 | \renewcommand\transparent[1]{}% 36 | }% 37 | \providecommand\rotatebox[2]{#2}% 38 | \newcommand*\fsize{\dimexpr\f@size pt\relax}% 39 | \newcommand*\lineheight[1]{\fontsize{\fsize}{#1\fsize}\selectfont}% 40 | \ifx\svgwidth\undefined% 41 | \setlength{\unitlength}{215.31401627bp}% 42 | \ifx\svgscale\undefined% 43 | \relax% 44 | \else% 45 | \setlength{\unitlength}{\unitlength * \real{\svgscale}}% 46 | \fi% 47 | \else% 48 | \setlength{\unitlength}{\svgwidth}% 49 | \fi% 50 | \global\let\svgwidth\undefined% 51 | \global\let\svgscale\undefined% 52 | \makeatother% 53 | \begin{picture}(1,0.70443348)% 54 | \lineheight{1}% 55 | \setlength\tabcolsep{0pt}% 56 | \put(0,0){\includegraphics[width=\unitlength,page=1]{handles-in-dimension-two-other-sphere.pdf}}% 57 | \end{picture}% 58 | \endgroup% 59 | -------------------------------------------------------------------------------- /thesis/figures/handles-in-dimension-two-torus-decomposition.pdf: -------------------------------------------------------------------------------- https://raw.githubusercontent.com/gillescastel/masterthesis/16b33d4121a8958e624bb0c9157151a63311b119/thesis/figures/handles-in-dimension-two-torus-decomposition.pdf -------------------------------------------------------------------------------- /thesis/figures/handles-in-dimension-two-torus-decomposition.pdf_tex: -------------------------------------------------------------------------------- 1 | %% Creator: Inkscape inkscape 0.92.4, www.inkscape.org 2 | %% PDF/EPS/PS + LaTeX output extension by Johan Engelen, 2010 3 | %% Accompanies image file 'handles-in-dimension-two-torus-decomposition.pdf' (pdf, eps, ps) 4 | %% 5 | %% To include the image in your LaTeX document, write 6 | %% \input{.pdf_tex} 7 | %% instead of 8 | %% \includegraphics{.pdf} 9 | %% To scale the image, write 10 | %% \def\svgwidth{} 11 | %% \input{.pdf_tex} 12 | %% instead of 13 | %% \includegraphics[width=]{.pdf} 14 | %% 15 | %% Images with a different path to the parent latex file can 16 | %% be accessed with the `import' package (which may need to be 17 | %% installed) using 18 | %% \usepackage{import} 19 | %% in the preamble, and then including the image with 20 | %% \import{}{.pdf_tex} 21 | %% Alternatively, one can specify 22 | %% \graphicspath{{/}} 23 | %% 24 | %% For more information, please see info/svg-inkscape on CTAN: 25 | %% http://tug.ctan.org/tex-archive/info/svg-inkscape 26 | %% 27 | \begingroup% 28 | \makeatletter% 29 | \providecommand\color[2][]{% 30 | \errmessage{(Inkscape) Color is used for the text in Inkscape, but the package 'color.sty' is not loaded}% 31 | \renewcommand\color[2][]{}% 32 | }% 33 | \providecommand\transparent[1]{% 34 | \errmessage{(Inkscape) Transparency is used (non-zero) for the text in Inkscape, but the package 'transparent.sty' is not loaded}% 35 | \renewcommand\transparent[1]{}% 36 | }% 37 | \providecommand\rotatebox[2]{#2}% 38 | \newcommand*\fsize{\dimexpr\f@size pt\relax}% 39 | \newcommand*\lineheight[1]{\fontsize{\fsize}{#1\fsize}\selectfont}% 40 | \ifx\svgwidth\undefined% 41 | \setlength{\unitlength}{243.12460832bp}% 42 | \ifx\svgscale\undefined% 43 | \relax% 44 | \else% 45 | \setlength{\unitlength}{\unitlength * \real{\svgscale}}% 46 | \fi% 47 | \else% 48 | \setlength{\unitlength}{\svgwidth}% 49 | \fi% 50 | \global\let\svgwidth\undefined% 51 | \global\let\svgscale\undefined% 52 | \makeatother% 53 | \begin{picture}(1,0.95811912)% 54 | \lineheight{1}% 55 | \setlength\tabcolsep{0pt}% 56 | \put(0,0){\includegraphics[width=\unitlength,page=1]{handles-in-dimension-two-torus-decomposition.pdf}}% 57 | \end{picture}% 58 | \endgroup% 59 | -------------------------------------------------------------------------------- /thesis/figures/heegaard-splittings-schemattically.pdf: -------------------------------------------------------------------------------- https://raw.githubusercontent.com/gillescastel/masterthesis/16b33d4121a8958e624bb0c9157151a63311b119/thesis/figures/heegaard-splittings-schemattically.pdf -------------------------------------------------------------------------------- /thesis/figures/homology-definition.pdf: -------------------------------------------------------------------------------- https://raw.githubusercontent.com/gillescastel/masterthesis/16b33d4121a8958e624bb0c9157151a63311b119/thesis/figures/homology-definition.pdf -------------------------------------------------------------------------------- /thesis/figures/idea-of-the-proof-maps-a-and-d.pdf: -------------------------------------------------------------------------------- https://raw.githubusercontent.com/gillescastel/masterthesis/16b33d4121a8958e624bb0c9157151a63311b119/thesis/figures/idea-of-the-proof-maps-a-and-d.pdf -------------------------------------------------------------------------------- /thesis/figures/idea-of-the-proof-maps-a-and-d.pdf_tex: -------------------------------------------------------------------------------- 1 | %% Creator: Inkscape inkscape 0.92.4, www.inkscape.org 2 | %% PDF/EPS/PS + LaTeX output extension by Johan Engelen, 2010 3 | %% Accompanies image file 'idea-of-the-proof-maps-a-and-d.pdf' (pdf, eps, ps) 4 | %% 5 | %% To include the image in your LaTeX document, write 6 | %% \input{.pdf_tex} 7 | %% instead of 8 | %% \includegraphics{.pdf} 9 | %% To scale the image, write 10 | %% \def\svgwidth{} 11 | %% \input{.pdf_tex} 12 | %% instead of 13 | %% \includegraphics[width=]{.pdf} 14 | %% 15 | %% Images with a different path to the parent latex file can 16 | %% be accessed with the `import' package (which may need to be 17 | %% installed) using 18 | %% \usepackage{import} 19 | %% in the preamble, and then including the image with 20 | %% \import{}{.pdf_tex} 21 | %% Alternatively, one can specify 22 | %% \graphicspath{{/}} 23 | %% 24 | %% For more information, please see info/svg-inkscape on CTAN: 25 | %% http://tug.ctan.org/tex-archive/info/svg-inkscape 26 | %% 27 | \begingroup% 28 | \makeatletter% 29 | \providecommand\color[2][]{% 30 | \errmessage{(Inkscape) Color is used for the text in Inkscape, but the package 'color.sty' is not loaded}% 31 | \renewcommand\color[2][]{}% 32 | }% 33 | \providecommand\transparent[1]{% 34 | \errmessage{(Inkscape) Transparency is used (non-zero) for the text in Inkscape, but the package 'transparent.sty' is not loaded}% 35 | \renewcommand\transparent[1]{}% 36 | }% 37 | \providecommand\rotatebox[2]{#2}% 38 | \newcommand*\fsize{\dimexpr\f@size pt\relax}% 39 | \newcommand*\lineheight[1]{\fontsize{\fsize}{#1\fsize}\selectfont}% 40 | \ifx\svgwidth\undefined% 41 | \setlength{\unitlength}{243.59689067bp}% 42 | \ifx\svgscale\undefined% 43 | \relax% 44 | \else% 45 | \setlength{\unitlength}{\unitlength * \real{\svgscale}}% 46 | \fi% 47 | \else% 48 | \setlength{\unitlength}{\svgwidth}% 49 | \fi% 50 | \global\let\svgwidth\undefined% 51 | \global\let\svgscale\undefined% 52 | \makeatother% 53 | \begin{picture}(1,0.69129482)% 54 | \lineheight{1}% 55 | \setlength\tabcolsep{0pt}% 56 | \put(0,0){\includegraphics[width=\unitlength,page=1]{idea-of-the-proof-maps-a-and-d.pdf}}% 57 | \put(0.44768,0.52776473){\color[rgb]{0,0,0}\makebox(0,0)[t]{\lineheight{1.25}\smash{\begin{tabular}[t]{c}$D$\end{tabular}}}}% 58 | \put(0,0){\includegraphics[width=\unitlength,page=2]{idea-of-the-proof-maps-a-and-d.pdf}}% 59 | \put(0.44768,0.17788542){\color[rgb]{0,0,0}\makebox(0,0)[t]{\lineheight{1.25}\smash{\begin{tabular}[t]{c}$A$\end{tabular}}}}% 60 | \put(0,0){\includegraphics[width=\unitlength,page=3]{idea-of-the-proof-maps-a-and-d.pdf}}% 61 | \end{picture}% 62 | \endgroup% 63 | -------------------------------------------------------------------------------- /thesis/figures/intersection-number.pdf: -------------------------------------------------------------------------------- https://raw.githubusercontent.com/gillescastel/masterthesis/16b33d4121a8958e624bb0c9157151a63311b119/thesis/figures/intersection-number.pdf -------------------------------------------------------------------------------- /thesis/figures/intersection-number.pdf_tex: -------------------------------------------------------------------------------- 1 | %% Creator: Inkscape inkscape 0.92.4, www.inkscape.org 2 | %% PDF/EPS/PS + LaTeX output extension by Johan Engelen, 2010 3 | %% Accompanies image file 'intersection-number.pdf' (pdf, eps, ps) 4 | %% 5 | %% To include the image in your LaTeX document, write 6 | %% \input{.pdf_tex} 7 | %% instead of 8 | %% \includegraphics{.pdf} 9 | %% To scale the image, write 10 | %% \def\svgwidth{} 11 | %% \input{.pdf_tex} 12 | %% instead of 13 | %% \includegraphics[width=]{.pdf} 14 | %% 15 | %% Images with a different path to the parent latex file can 16 | %% be accessed with the `import' package (which may need to be 17 | %% installed) using 18 | %% \usepackage{import} 19 | %% in the preamble, and then including the image with 20 | %% \import{}{.pdf_tex} 21 | %% Alternatively, one can specify 22 | %% \graphicspath{{/}} 23 | %% 24 | %% For more information, please see info/svg-inkscape on CTAN: 25 | %% http://tug.ctan.org/tex-archive/info/svg-inkscape 26 | %% 27 | \begingroup% 28 | \makeatletter% 29 | \providecommand\color[2][]{% 30 | \errmessage{(Inkscape) Color is used for the text in Inkscape, but the package 'color.sty' is not loaded}% 31 | \renewcommand\color[2][]{}% 32 | }% 33 | \providecommand\transparent[1]{% 34 | \errmessage{(Inkscape) Transparency is used (non-zero) for the text in Inkscape, but the package 'transparent.sty' is not loaded}% 35 | \renewcommand\transparent[1]{}% 36 | }% 37 | \providecommand\rotatebox[2]{#2}% 38 | \newcommand*\fsize{\dimexpr\f@size pt\relax}% 39 | \newcommand*\lineheight[1]{\fontsize{\fsize}{#1\fsize}\selectfont}% 40 | \ifx\svgwidth\undefined% 41 | \setlength{\unitlength}{173.87923113bp}% 42 | \ifx\svgscale\undefined% 43 | \relax% 44 | \else% 45 | \setlength{\unitlength}{\unitlength * \real{\svgscale}}% 46 | \fi% 47 | \else% 48 | \setlength{\unitlength}{\svgwidth}% 49 | \fi% 50 | \global\let\svgwidth\undefined% 51 | \global\let\svgscale\undefined% 52 | \makeatother% 53 | \begin{picture}(1,0.86354902)% 54 | \lineheight{1}% 55 | \setlength\tabcolsep{0pt}% 56 | \put(0,0){\includegraphics[width=\unitlength,page=1]{intersection-number.pdf}}% 57 | \put(0.3757951,0.71581607){\color[rgb]{0,0,0}\makebox(0,0)[lt]{\lineheight{1.25}\smash{\begin{tabular}[t]{l}$M'$\end{tabular}}}}% 58 | \put(0,0){\includegraphics[width=\unitlength,page=2]{intersection-number.pdf}}% 59 | \put(0.48333632,0.56842175){\color[rgb]{0,0,0}\makebox(0,0)[lt]{\lineheight{1.25}\smash{\begin{tabular}[t]{l}$M$\end{tabular}}}}% 60 | \put(0.163742,0.53638514){\color[rgb]{0,0,0}\makebox(0,0)[lt]{\lineheight{1.25}\smash{\begin{tabular}[t]{l}$-1$\end{tabular}}}}% 61 | \put(0.69887945,0.48504617){\color[rgb]{0,0,0}\makebox(0,0)[lt]{\lineheight{1.25}\smash{\begin{tabular}[t]{l}$+1$\end{tabular}}}}% 62 | \put(0,0){\includegraphics[width=\unitlength,page=3]{intersection-number.pdf}}% 63 | \end{picture}% 64 | \endgroup% 65 | -------------------------------------------------------------------------------- /thesis/figures/intersection-of-manifolds-is-not-always-a-manifold.pdf: -------------------------------------------------------------------------------- https://raw.githubusercontent.com/gillescastel/masterthesis/16b33d4121a8958e624bb0c9157151a63311b119/thesis/figures/intersection-of-manifolds-is-not-always-a-manifold.pdf -------------------------------------------------------------------------------- /thesis/figures/intersection-of-manifolds-is-not-always-a-manifold.pdf_tex: -------------------------------------------------------------------------------- 1 | %% Creator: Inkscape inkscape 0.92.4, www.inkscape.org 2 | %% PDF/EPS/PS + LaTeX output extension by Johan Engelen, 2010 3 | %% Accompanies image file 'intersection-of-manifolds-is-not-always-a-manifold.pdf' (pdf, eps, ps) 4 | %% 5 | %% To include the image in your LaTeX document, write 6 | %% \input{.pdf_tex} 7 | %% instead of 8 | %% \includegraphics{.pdf} 9 | %% To scale the image, write 10 | %% \def\svgwidth{} 11 | %% \input{.pdf_tex} 12 | %% instead of 13 | %% \includegraphics[width=]{.pdf} 14 | %% 15 | %% Images with a different path to the parent latex file can 16 | %% be accessed with the `import' package (which may need to be 17 | %% installed) using 18 | %% \usepackage{import} 19 | %% in the preamble, and then including the image with 20 | %% \import{}{.pdf_tex} 21 | %% Alternatively, one can specify 22 | %% \graphicspath{{/}} 23 | %% 24 | %% For more information, please see info/svg-inkscape on CTAN: 25 | %% http://tug.ctan.org/tex-archive/info/svg-inkscape 26 | %% 27 | \begingroup% 28 | \makeatletter% 29 | \providecommand\color[2][]{% 30 | \errmessage{(Inkscape) Color is used for the text in Inkscape, but the package 'color.sty' is not loaded}% 31 | \renewcommand\color[2][]{}% 32 | }% 33 | \providecommand\transparent[1]{% 34 | \errmessage{(Inkscape) Transparency is used (non-zero) for the text in Inkscape, but the package 'transparent.sty' is not loaded}% 35 | \renewcommand\transparent[1]{}% 36 | }% 37 | \providecommand\rotatebox[2]{#2}% 38 | \newcommand*\fsize{\dimexpr\f@size pt\relax}% 39 | \newcommand*\lineheight[1]{\fontsize{\fsize}{#1\fsize}\selectfont}% 40 | \ifx\svgwidth\undefined% 41 | \setlength{\unitlength}{141.06406385bp}% 42 | \ifx\svgscale\undefined% 43 | \relax% 44 | \else% 45 | \setlength{\unitlength}{\unitlength * \real{\svgscale}}% 46 | \fi% 47 | \else% 48 | \setlength{\unitlength}{\svgwidth}% 49 | \fi% 50 | \global\let\svgwidth\undefined% 51 | \global\let\svgscale\undefined% 52 | \makeatother% 53 | \begin{picture}(1,0.56899231)% 54 | \lineheight{1}% 55 | \setlength\tabcolsep{0pt}% 56 | \put(0,0){\includegraphics[width=\unitlength,page=1]{intersection-of-manifolds-is-not-always-a-manifold.pdf}}% 57 | \put(0.02567702,0.36393797){\color[rgb]{0,0,0}\makebox(0,0)[lt]{\lineheight{1.25}\smash{\begin{tabular}[t]{l}$N_1$\end{tabular}}}}% 58 | \put(0.02567702,0.21437572){\color[rgb]{0,0,0}\makebox(0,0)[lt]{\lineheight{1.25}\smash{\begin{tabular}[t]{l}$N_2$\end{tabular}}}}% 59 | \put(0.02567702,0.02550859){\color[rgb]{0,0,0}\makebox(0,0)[lt]{\lineheight{1.25}\smash{\begin{tabular}[t]{l}$N_1 \cap N_2$\end{tabular}}}}% 60 | \put(0.02567702,0.48484706){\color[rgb]{0,0,0}\makebox(0,0)[lt]{\lineheight{1.25}\smash{\begin{tabular}[t]{l}$M = \R^2$\end{tabular}}}}% 61 | \end{picture}% 62 | \endgroup% 63 | -------------------------------------------------------------------------------- /thesis/figures/intersection-points-cancellation.pdf: -------------------------------------------------------------------------------- https://raw.githubusercontent.com/gillescastel/masterthesis/16b33d4121a8958e624bb0c9157151a63311b119/thesis/figures/intersection-points-cancellation.pdf -------------------------------------------------------------------------------- /thesis/figures/isotopy-between-circle-and-other-circle.pdf: -------------------------------------------------------------------------------- https://raw.githubusercontent.com/gillescastel/masterthesis/16b33d4121a8958e624bb0c9157151a63311b119/thesis/figures/isotopy-between-circle-and-other-circle.pdf -------------------------------------------------------------------------------- /thesis/figures/isotopy-between-circle-and-other-circle.pdf_tex: -------------------------------------------------------------------------------- 1 | %% Creator: Inkscape inkscape 0.92.4, www.inkscape.org 2 | %% PDF/EPS/PS + LaTeX output extension by Johan Engelen, 2010 3 | %% Accompanies image file 'isotopy-between-circle-and-other-circle.pdf' (pdf, eps, ps) 4 | %% 5 | %% To include the image in your LaTeX document, write 6 | %% \input{.pdf_tex} 7 | %% instead of 8 | %% \includegraphics{.pdf} 9 | %% To scale the image, write 10 | %% \def\svgwidth{} 11 | %% \input{.pdf_tex} 12 | %% instead of 13 | %% \includegraphics[width=]{.pdf} 14 | %% 15 | %% Images with a different path to the parent latex file can 16 | %% be accessed with the `import' package (which may need to be 17 | %% installed) using 18 | %% \usepackage{import} 19 | %% in the preamble, and then including the image with 20 | %% \import{}{.pdf_tex} 21 | %% Alternatively, one can specify 22 | %% \graphicspath{{/}} 23 | %% 24 | %% For more information, please see info/svg-inkscape on CTAN: 25 | %% http://tug.ctan.org/tex-archive/info/svg-inkscape 26 | %% 27 | \begingroup% 28 | \makeatletter% 29 | \providecommand\color[2][]{% 30 | \errmessage{(Inkscape) Color is used for the text in Inkscape, but the package 'color.sty' is not loaded}% 31 | \renewcommand\color[2][]{}% 32 | }% 33 | \providecommand\transparent[1]{% 34 | \errmessage{(Inkscape) Transparency is used (non-zero) for the text in Inkscape, but the package 'transparent.sty' is not loaded}% 35 | \renewcommand\transparent[1]{}% 36 | }% 37 | \providecommand\rotatebox[2]{#2}% 38 | \newcommand*\fsize{\dimexpr\f@size pt\relax}% 39 | \newcommand*\lineheight[1]{\fontsize{\fsize}{#1\fsize}\selectfont}% 40 | \ifx\svgwidth\undefined% 41 | \setlength{\unitlength}{643.41162494bp}% 42 | \ifx\svgscale\undefined% 43 | \relax% 44 | \else% 45 | \setlength{\unitlength}{\unitlength * \real{\svgscale}}% 46 | \fi% 47 | \else% 48 | \setlength{\unitlength}{\svgwidth}% 49 | \fi% 50 | \global\let\svgwidth\undefined% 51 | \global\let\svgscale\undefined% 52 | \makeatother% 53 | \begin{picture}(1,0.12286879)% 54 | \lineheight{1}% 55 | \setlength\tabcolsep{0pt}% 56 | \put(0,0){\includegraphics[width=\unitlength,page=1]{isotopy-between-circle-and-other-circle.pdf}}% 57 | \end{picture}% 58 | \endgroup% 59 | -------------------------------------------------------------------------------- /thesis/figures/kunneth-formula.pdf: -------------------------------------------------------------------------------- https://raw.githubusercontent.com/gillescastel/masterthesis/16b33d4121a8958e624bb0c9157151a63311b119/thesis/figures/kunneth-formula.pdf -------------------------------------------------------------------------------- /thesis/figures/l-bar-last-condition-of-manifold-with-boundary.pdf: -------------------------------------------------------------------------------- https://raw.githubusercontent.com/gillescastel/masterthesis/16b33d4121a8958e624bb0c9157151a63311b119/thesis/figures/l-bar-last-condition-of-manifold-with-boundary.pdf -------------------------------------------------------------------------------- /thesis/figures/l-bar-last-condition-of-manifold-with-boundary.pdf_tex: -------------------------------------------------------------------------------- 1 | %% Creator: Inkscape inkscape 0.92.4, www.inkscape.org 2 | %% PDF/EPS/PS + LaTeX output extension by Johan Engelen, 2010 3 | %% Accompanies image file 'l-bar-last-condition-of-manifold-with-boundary.pdf' (pdf, eps, ps) 4 | %% 5 | %% To include the image in your LaTeX document, write 6 | %% \input{.pdf_tex} 7 | %% instead of 8 | %% \includegraphics{.pdf} 9 | %% To scale the image, write 10 | %% \def\svgwidth{} 11 | %% \input{.pdf_tex} 12 | %% instead of 13 | %% \includegraphics[width=]{.pdf} 14 | %% 15 | %% Images with a different path to the parent latex file can 16 | %% be accessed with the `import' package (which may need to be 17 | %% installed) using 18 | %% \usepackage{import} 19 | %% in the preamble, and then including the image with 20 | %% \import{}{.pdf_tex} 21 | %% Alternatively, one can specify 22 | %% \graphicspath{{/}} 23 | %% 24 | %% For more information, please see info/svg-inkscape on CTAN: 25 | %% http://tug.ctan.org/tex-archive/info/svg-inkscape 26 | %% 27 | \begingroup% 28 | \makeatletter% 29 | \providecommand\color[2][]{% 30 | \errmessage{(Inkscape) Color is used for the text in Inkscape, but the package 'color.sty' is not loaded}% 31 | \renewcommand\color[2][]{}% 32 | }% 33 | \providecommand\transparent[1]{% 34 | \errmessage{(Inkscape) Transparency is used (non-zero) for the text in Inkscape, but the package 'transparent.sty' is not loaded}% 35 | \renewcommand\transparent[1]{}% 36 | }% 37 | \providecommand\rotatebox[2]{#2}% 38 | \newcommand*\fsize{\dimexpr\f@size pt\relax}% 39 | \newcommand*\lineheight[1]{\fontsize{\fsize}{#1\fsize}\selectfont}% 40 | \ifx\svgwidth\undefined% 41 | \setlength{\unitlength}{159.4024514bp}% 42 | \ifx\svgscale\undefined% 43 | \relax% 44 | \else% 45 | \setlength{\unitlength}{\unitlength * \real{\svgscale}}% 46 | \fi% 47 | \else% 48 | \setlength{\unitlength}{\svgwidth}% 49 | \fi% 50 | \global\let\svgwidth\undefined% 51 | \global\let\svgscale\undefined% 52 | \makeatother% 53 | \begin{picture}(1,0.04358239)% 54 | \lineheight{1}% 55 | \setlength\tabcolsep{0pt}% 56 | \put(0,0){\includegraphics[width=\unitlength,page=1]{l-bar-last-condition-of-manifold-with-boundary.pdf}}% 57 | \end{picture}% 58 | \endgroup% 59 | -------------------------------------------------------------------------------- /thesis/figures/l-bar-manifold-2-dimensional-case-part-flow.pdf: -------------------------------------------------------------------------------- https://raw.githubusercontent.com/gillescastel/masterthesis/16b33d4121a8958e624bb0c9157151a63311b119/thesis/figures/l-bar-manifold-2-dimensional-case-part-flow.pdf -------------------------------------------------------------------------------- /thesis/figures/l-bar-manifold-2-dimensional-case.pdf: -------------------------------------------------------------------------------- https://raw.githubusercontent.com/gillescastel/masterthesis/16b33d4121a8958e624bb0c9157151a63311b119/thesis/figures/l-bar-manifold-2-dimensional-case.pdf -------------------------------------------------------------------------------- /thesis/figures/lbar-manifold-three-dimensional-case.pdf: -------------------------------------------------------------------------------- https://raw.githubusercontent.com/gillescastel/masterthesis/16b33d4121a8958e624bb0c9157151a63311b119/thesis/figures/lbar-manifold-three-dimensional-case.pdf -------------------------------------------------------------------------------- /thesis/figures/lemma-partial-squared-zero-proof.pdf: -------------------------------------------------------------------------------- https://raw.githubusercontent.com/gillescastel/masterthesis/16b33d4121a8958e624bb0c9157151a63311b119/thesis/figures/lemma-partial-squared-zero-proof.pdf -------------------------------------------------------------------------------- /thesis/figures/lemma-partial-squared-zero-proof.pdf_tex: -------------------------------------------------------------------------------- 1 | %% Creator: Inkscape inkscape 0.92.4, www.inkscape.org 2 | %% PDF/EPS/PS + LaTeX output extension by Johan Engelen, 2010 3 | %% Accompanies image file 'lemma-partial-squared-zero-proof.pdf' (pdf, eps, ps) 4 | %% 5 | %% To include the image in your LaTeX document, write 6 | %% \input{.pdf_tex} 7 | %% instead of 8 | %% \includegraphics{.pdf} 9 | %% To scale the image, write 10 | %% \def\svgwidth{} 11 | %% \input{.pdf_tex} 12 | %% instead of 13 | %% \includegraphics[width=]{.pdf} 14 | %% 15 | %% Images with a different path to the parent latex file can 16 | %% be accessed with the `import' package (which may need to be 17 | %% installed) using 18 | %% \usepackage{import} 19 | %% in the preamble, and then including the image with 20 | %% \import{}{.pdf_tex} 21 | %% Alternatively, one can specify 22 | %% \graphicspath{{/}} 23 | %% 24 | %% For more information, please see info/svg-inkscape on CTAN: 25 | %% http://tug.ctan.org/tex-archive/info/svg-inkscape 26 | %% 27 | \begingroup% 28 | \makeatletter% 29 | \providecommand\color[2][]{% 30 | \errmessage{(Inkscape) Color is used for the text in Inkscape, but the package 'color.sty' is not loaded}% 31 | \renewcommand\color[2][]{}% 32 | }% 33 | \providecommand\transparent[1]{% 34 | \errmessage{(Inkscape) Transparency is used (non-zero) for the text in Inkscape, but the package 'transparent.sty' is not loaded}% 35 | \renewcommand\transparent[1]{}% 36 | }% 37 | \providecommand\rotatebox[2]{#2}% 38 | \newcommand*\fsize{\dimexpr\f@size pt\relax}% 39 | \newcommand*\lineheight[1]{\fontsize{\fsize}{#1\fsize}\selectfont}% 40 | \ifx\svgwidth\undefined% 41 | \setlength{\unitlength}{253.82388618bp}% 42 | \ifx\svgscale\undefined% 43 | \relax% 44 | \else% 45 | \setlength{\unitlength}{\unitlength * \real{\svgscale}}% 46 | \fi% 47 | \else% 48 | \setlength{\unitlength}{\svgwidth}% 49 | \fi% 50 | \global\let\svgwidth\undefined% 51 | \global\let\svgscale\undefined% 52 | \makeatother% 53 | \begin{picture}(1,0.69244748)% 54 | \lineheight{1}% 55 | \setlength\tabcolsep{0pt}% 56 | \put(0,0){\includegraphics[width=\unitlength,page=1]{lemma-partial-squared-zero-proof.pdf}}% 57 | \put(0.24283533,0.61071401){\color[rgb]{0,0,0}\makebox(0,0)[lt]{\lineheight{1.25}\smash{\begin{tabular}[t]{l}$x_n$\end{tabular}}}}% 58 | \put(0.65279377,0.53093714){\color[rgb]{0,0,0}\makebox(0,0)[lt]{\lineheight{1.25}\smash{\begin{tabular}[t]{l}$x$\end{tabular}}}}% 59 | \put(0,0){\includegraphics[width=\unitlength,page=2]{lemma-partial-squared-zero-proof.pdf}}% 60 | \put(0.69541638,0.14252448){\color[rgb]{0,0,0}\makebox(0,0)[lt]{\lineheight{1.25}\smash{\begin{tabular}[t]{l}$y$\end{tabular}}}}% 61 | \put(0.43392245,0.13769567){\color[rgb]{0,0,0}\makebox(0,0)[lt]{\lineheight{1.25}\smash{\begin{tabular}[t]{l}$y_n$\end{tabular}}}}% 62 | \put(0.84903331,0.10465418){\color[rgb]{0,0,0}\makebox(0,0)[lt]{\lineheight{1.25}\smash{\begin{tabular}[t]{l}$f(y)$\end{tabular}}}}% 63 | \end{picture}% 64 | \endgroup% 65 | -------------------------------------------------------------------------------- /thesis/figures/lemma-sphere-connect-with-tube-proof.pdf: -------------------------------------------------------------------------------- https://raw.githubusercontent.com/gillescastel/masterthesis/16b33d4121a8958e624bb0c9157151a63311b119/thesis/figures/lemma-sphere-connect-with-tube-proof.pdf -------------------------------------------------------------------------------- /thesis/figures/lemma-sphere-connect-with-tube.pdf: -------------------------------------------------------------------------------- https://raw.githubusercontent.com/gillescastel/masterthesis/16b33d4121a8958e624bb0c9157151a63311b119/thesis/figures/lemma-sphere-connect-with-tube.pdf -------------------------------------------------------------------------------- /thesis/figures/level-sets-of-distance-function-torus.pdf: -------------------------------------------------------------------------------- https://raw.githubusercontent.com/gillescastel/masterthesis/16b33d4121a8958e624bb0c9157151a63311b119/thesis/figures/level-sets-of-distance-function-torus.pdf -------------------------------------------------------------------------------- /thesis/figures/level-sets-of-distance-function-torus.pdf_tex: -------------------------------------------------------------------------------- 1 | %% Creator: Inkscape inkscape 0.92.4, www.inkscape.org 2 | %% PDF/EPS/PS + LaTeX output extension by Johan Engelen, 2010 3 | %% Accompanies image file 'level-sets-of-distance-function-torus.pdf' (pdf, eps, ps) 4 | %% 5 | %% To include the image in your LaTeX document, write 6 | %% \input{.pdf_tex} 7 | %% instead of 8 | %% \includegraphics{.pdf} 9 | %% To scale the image, write 10 | %% \def\svgwidth{} 11 | %% \input{.pdf_tex} 12 | %% instead of 13 | %% \includegraphics[width=]{.pdf} 14 | %% 15 | %% Images with a different path to the parent latex file can 16 | %% be accessed with the `import' package (which may need to be 17 | %% installed) using 18 | %% \usepackage{import} 19 | %% in the preamble, and then including the image with 20 | %% \import{}{.pdf_tex} 21 | %% Alternatively, one can specify 22 | %% \graphicspath{{/}} 23 | %% 24 | %% For more information, please see info/svg-inkscape on CTAN: 25 | %% http://tug.ctan.org/tex-archive/info/svg-inkscape 26 | %% 27 | \begingroup% 28 | \makeatletter% 29 | \providecommand\color[2][]{% 30 | \errmessage{(Inkscape) Color is used for the text in Inkscape, but the package 'color.sty' is not loaded}% 31 | \renewcommand\color[2][]{}% 32 | }% 33 | \providecommand\transparent[1]{% 34 | \errmessage{(Inkscape) Transparency is used (non-zero) for the text in Inkscape, but the package 'transparent.sty' is not loaded}% 35 | \renewcommand\transparent[1]{}% 36 | }% 37 | \providecommand\rotatebox[2]{#2}% 38 | \newcommand*\fsize{\dimexpr\f@size pt\relax}% 39 | \newcommand*\lineheight[1]{\fontsize{\fsize}{#1\fsize}\selectfont}% 40 | \ifx\svgwidth\undefined% 41 | \setlength{\unitlength}{185.32860703bp}% 42 | \ifx\svgscale\undefined% 43 | \relax% 44 | \else% 45 | \setlength{\unitlength}{\unitlength * \real{\svgscale}}% 46 | \fi% 47 | \else% 48 | \setlength{\unitlength}{\svgwidth}% 49 | \fi% 50 | \global\let\svgwidth\undefined% 51 | \global\let\svgscale\undefined% 52 | \makeatother% 53 | \begin{picture}(1,0.95395581)% 54 | \lineheight{1}% 55 | \setlength\tabcolsep{0pt}% 56 | \put(0,0){\includegraphics[width=\unitlength,page=1]{level-sets-of-distance-function-torus.pdf}}% 57 | \put(0.88080793,0.16776051){\color[rgb]{0,0,0}\makebox(0,0)[lt]{\lineheight{1.25}\smash{\begin{tabular}[t]{l}$p$\end{tabular}}}}% 58 | \put(0,0){\includegraphics[width=\unitlength,page=2]{level-sets-of-distance-function-torus.pdf}}% 59 | \end{picture}% 60 | \endgroup% 61 | -------------------------------------------------------------------------------- /thesis/figures/linear-map-rank-nullity-theorem.pdf: -------------------------------------------------------------------------------- https://raw.githubusercontent.com/gillescastel/masterthesis/16b33d4121a8958e624bb0c9157151a63311b119/thesis/figures/linear-map-rank-nullity-theorem.pdf -------------------------------------------------------------------------------- /thesis/figures/local-model.pdf: -------------------------------------------------------------------------------- https://raw.githubusercontent.com/gillescastel/masterthesis/16b33d4121a8958e624bb0c9157151a63311b119/thesis/figures/local-model.pdf -------------------------------------------------------------------------------- /thesis/figures/mathcal-m-trajectories-other-sphere-only-m.pdf: -------------------------------------------------------------------------------- https://raw.githubusercontent.com/gillescastel/masterthesis/16b33d4121a8958e624bb0c9157151a63311b119/thesis/figures/mathcal-m-trajectories-other-sphere-only-m.pdf -------------------------------------------------------------------------------- /thesis/figures/mathcal-m-trajectories-other-sphere.pdf: -------------------------------------------------------------------------------- https://raw.githubusercontent.com/gillescastel/masterthesis/16b33d4121a8958e624bb0c9157151a63311b119/thesis/figures/mathcal-m-trajectories-other-sphere.pdf -------------------------------------------------------------------------------- /thesis/figures/mayer-vietoris-example.pdf: -------------------------------------------------------------------------------- https://raw.githubusercontent.com/gillescastel/masterthesis/16b33d4121a8958e624bb0c9157151a63311b119/thesis/figures/mayer-vietoris-example.pdf -------------------------------------------------------------------------------- /thesis/figures/mayer-vietoris-example.pdf_tex: -------------------------------------------------------------------------------- 1 | %% Creator: Inkscape inkscape 0.92.4, www.inkscape.org 2 | %% PDF/EPS/PS + LaTeX output extension by Johan Engelen, 2010 3 | %% Accompanies image file 'mayer-vietoris-example.pdf' (pdf, eps, ps) 4 | %% 5 | %% To include the image in your LaTeX document, write 6 | %% \input{.pdf_tex} 7 | %% instead of 8 | %% \includegraphics{.pdf} 9 | %% To scale the image, write 10 | %% \def\svgwidth{} 11 | %% \input{.pdf_tex} 12 | %% instead of 13 | %% \includegraphics[width=]{.pdf} 14 | %% 15 | %% Images with a different path to the parent latex file can 16 | %% be accessed with the `import' package (which may need to be 17 | %% installed) using 18 | %% \usepackage{import} 19 | %% in the preamble, and then including the image with 20 | %% \import{}{.pdf_tex} 21 | %% Alternatively, one can specify 22 | %% \graphicspath{{/}} 23 | %% 24 | %% For more information, please see info/svg-inkscape on CTAN: 25 | %% http://tug.ctan.org/tex-archive/info/svg-inkscape 26 | %% 27 | \begingroup% 28 | \makeatletter% 29 | \providecommand\color[2][]{% 30 | \errmessage{(Inkscape) Color is used for the text in Inkscape, but the package 'color.sty' is not loaded}% 31 | \renewcommand\color[2][]{}% 32 | }% 33 | \providecommand\transparent[1]{% 34 | \errmessage{(Inkscape) Transparency is used (non-zero) for the text in Inkscape, but the package 'transparent.sty' is not loaded}% 35 | \renewcommand\transparent[1]{}% 36 | }% 37 | \providecommand\rotatebox[2]{#2}% 38 | \newcommand*\fsize{\dimexpr\f@size pt\relax}% 39 | \newcommand*\lineheight[1]{\fontsize{\fsize}{#1\fsize}\selectfont}% 40 | \ifx\svgwidth\undefined% 41 | \setlength{\unitlength}{125.55745643bp}% 42 | \ifx\svgscale\undefined% 43 | \relax% 44 | \else% 45 | \setlength{\unitlength}{\unitlength * \real{\svgscale}}% 46 | \fi% 47 | \else% 48 | \setlength{\unitlength}{\svgwidth}% 49 | \fi% 50 | \global\let\svgwidth\undefined% 51 | \global\let\svgscale\undefined% 52 | \makeatother% 53 | \begin{picture}(1,0.49821184)% 54 | \lineheight{1}% 55 | \setlength\tabcolsep{0pt}% 56 | \put(0,0){\includegraphics[width=\unitlength,page=1]{mayer-vietoris-example.pdf}}% 57 | \put(0.70461728,0.36087343){\color[rgb]{0,0,0}\makebox(0,0)[lt]{\lineheight{1.25}\smash{\begin{tabular}[t]{l}$B$\end{tabular}}}}% 58 | \put(0,0){\includegraphics[width=\unitlength,page=2]{mayer-vietoris-example.pdf}}% 59 | \put(0.70461728,0.44815517){\color[rgb]{0,0,0}\makebox(0,0)[lt]{\lineheight{1.25}\smash{\begin{tabular}[t]{l}$A$\end{tabular}}}}% 60 | \put(0,0){\includegraphics[width=\unitlength,page=3]{mayer-vietoris-example.pdf}}% 61 | \put(0.07711851,0.27677189){\color[rgb]{0,0,0}\makebox(0,0)[lt]{\lineheight{1.25}\smash{\begin{tabular}[t]{l}$\rho$\end{tabular}}}}% 62 | \put(0.53849457,0.20318405){\color[rgb]{0,0,0}\makebox(0,0)[lt]{\lineheight{1.25}\smash{\begin{tabular}[t]{l}$\sigma$\end{tabular}}}}% 63 | \put(0.70461728,0.28285543){\color[rgb]{0,0,0}\makebox(0,0)[lt]{\lineheight{1.25}\smash{\begin{tabular}[t]{l}$A \cap B$\end{tabular}}}}% 64 | \put(0,0){\includegraphics[width=\unitlength,page=4]{mayer-vietoris-example.pdf}}% 65 | \end{picture}% 66 | \endgroup% 67 | -------------------------------------------------------------------------------- /thesis/figures/more-concrete-morse-charts.pdf: -------------------------------------------------------------------------------- https://raw.githubusercontent.com/gillescastel/masterthesis/16b33d4121a8958e624bb0c9157151a63311b119/thesis/figures/more-concrete-morse-charts.pdf -------------------------------------------------------------------------------- /thesis/figures/mores-homology-three-torus-critical-points-graph.pdf: -------------------------------------------------------------------------------- https://raw.githubusercontent.com/gillescastel/masterthesis/16b33d4121a8958e624bb0c9157151a63311b119/thesis/figures/mores-homology-three-torus-critical-points-graph.pdf -------------------------------------------------------------------------------- /thesis/figures/mores-homology-three-torus-critical-points-graph.pdf_tex: -------------------------------------------------------------------------------- 1 | %% Creator: Inkscape inkscape 0.92.4, www.inkscape.org 2 | %% PDF/EPS/PS + LaTeX output extension by Johan Engelen, 2010 3 | %% Accompanies image file 'mores-homology-three-torus-critical-points-graph.pdf' (pdf, eps, ps) 4 | %% 5 | %% To include the image in your LaTeX document, write 6 | %% \input{.pdf_tex} 7 | %% instead of 8 | %% \includegraphics{.pdf} 9 | %% To scale the image, write 10 | %% \def\svgwidth{} 11 | %% \input{.pdf_tex} 12 | %% instead of 13 | %% \includegraphics[width=]{.pdf} 14 | %% 15 | %% Images with a different path to the parent latex file can 16 | %% be accessed with the `import' package (which may need to be 17 | %% installed) using 18 | %% \usepackage{import} 19 | %% in the preamble, and then including the image with 20 | %% \import{}{.pdf_tex} 21 | %% Alternatively, one can specify 22 | %% \graphicspath{{/}} 23 | %% 24 | %% For more information, please see info/svg-inkscape on CTAN: 25 | %% http://tug.ctan.org/tex-archive/info/svg-inkscape 26 | %% 27 | \begingroup% 28 | \makeatletter% 29 | \providecommand\color[2][]{% 30 | \errmessage{(Inkscape) Color is used for the text in Inkscape, but the package 'color.sty' is not loaded}% 31 | \renewcommand\color[2][]{}% 32 | }% 33 | \providecommand\transparent[1]{% 34 | \errmessage{(Inkscape) Transparency is used (non-zero) for the text in Inkscape, but the package 'transparent.sty' is not loaded}% 35 | \renewcommand\transparent[1]{}% 36 | }% 37 | \providecommand\rotatebox[2]{#2}% 38 | \newcommand*\fsize{\dimexpr\f@size pt\relax}% 39 | \newcommand*\lineheight[1]{\fontsize{\fsize}{#1\fsize}\selectfont}% 40 | \ifx\svgwidth\undefined% 41 | \setlength{\unitlength}{162.16234462bp}% 42 | \ifx\svgscale\undefined% 43 | \relax% 44 | \else% 45 | \setlength{\unitlength}{\unitlength * \real{\svgscale}}% 46 | \fi% 47 | \else% 48 | \setlength{\unitlength}{\svgwidth}% 49 | \fi% 50 | \global\let\svgwidth\undefined% 51 | \global\let\svgscale\undefined% 52 | \makeatother% 53 | \begin{picture}(1,0.71395348)% 54 | \lineheight{1}% 55 | \setlength\tabcolsep{0pt}% 56 | \put(0,0){\includegraphics[width=\unitlength,page=1]{mores-homology-three-torus-critical-points-graph.pdf}}% 57 | \end{picture}% 58 | \endgroup% 59 | -------------------------------------------------------------------------------- /thesis/figures/morse-chain-complex-visualized-truncated.pdf: -------------------------------------------------------------------------------- https://raw.githubusercontent.com/gillescastel/masterthesis/16b33d4121a8958e624bb0c9157151a63311b119/thesis/figures/morse-chain-complex-visualized-truncated.pdf -------------------------------------------------------------------------------- /thesis/figures/morse-chain-complex-visualized-truncated.pdf_tex: -------------------------------------------------------------------------------- 1 | %% Creator: Inkscape inkscape 0.92.4, www.inkscape.org 2 | %% PDF/EPS/PS + LaTeX output extension by Johan Engelen, 2010 3 | %% Accompanies image file 'morse-chain-complex-visualized-truncated.pdf' (pdf, eps, ps) 4 | %% 5 | %% To include the image in your LaTeX document, write 6 | %% \input{.pdf_tex} 7 | %% instead of 8 | %% \includegraphics{.pdf} 9 | %% To scale the image, write 10 | %% \def\svgwidth{} 11 | %% \input{.pdf_tex} 12 | %% instead of 13 | %% \includegraphics[width=]{.pdf} 14 | %% 15 | %% Images with a different path to the parent latex file can 16 | %% be accessed with the `import' package (which may need to be 17 | %% installed) using 18 | %% \usepackage{import} 19 | %% in the preamble, and then including the image with 20 | %% \import{}{.pdf_tex} 21 | %% Alternatively, one can specify 22 | %% \graphicspath{{/}} 23 | %% 24 | %% For more information, please see info/svg-inkscape on CTAN: 25 | %% http://tug.ctan.org/tex-archive/info/svg-inkscape 26 | %% 27 | \begingroup% 28 | \makeatletter% 29 | \providecommand\color[2][]{% 30 | \errmessage{(Inkscape) Color is used for the text in Inkscape, but the package 'color.sty' is not loaded}% 31 | \renewcommand\color[2][]{}% 32 | }% 33 | \providecommand\transparent[1]{% 34 | \errmessage{(Inkscape) Transparency is used (non-zero) for the text in Inkscape, but the package 'transparent.sty' is not loaded}% 35 | \renewcommand\transparent[1]{}% 36 | }% 37 | \providecommand\rotatebox[2]{#2}% 38 | \newcommand*\fsize{\dimexpr\f@size pt\relax}% 39 | \newcommand*\lineheight[1]{\fontsize{\fsize}{#1\fsize}\selectfont}% 40 | \ifx\svgwidth\undefined% 41 | \setlength{\unitlength}{479.29551973bp}% 42 | \ifx\svgscale\undefined% 43 | \relax% 44 | \else% 45 | \setlength{\unitlength}{\unitlength * \real{\svgscale}}% 46 | \fi% 47 | \else% 48 | \setlength{\unitlength}{\svgwidth}% 49 | \fi% 50 | \global\let\svgwidth\undefined% 51 | \global\let\svgscale\undefined% 52 | \makeatother% 53 | \begin{picture}(1,0.63254613)% 54 | \lineheight{1}% 55 | \setlength\tabcolsep{0pt}% 56 | \put(0.39177369,0.61832901){\color[rgb]{0,0,0}\makebox(0,0)[t]{\lineheight{1.25}\smash{\begin{tabular}[t]{c}$C_2$\end{tabular}}}}% 57 | \put(0.56925556,0.00419492){\color[rgb]{0,0,0}\makebox(0,0)[t]{\lineheight{1.25}\smash{\begin{tabular}[t]{c}$C_1$\end{tabular}}}}% 58 | \put(0.74729377,0.5797745){\color[rgb]{0,0,0}\makebox(0,0)[t]{\lineheight{1.25}\smash{\begin{tabular}[t]{c}$C_0$\end{tabular}}}}% 59 | \put(0.92477557,0.28726719){\color[rgb]{0,0,0}\makebox(0,0)[t]{\lineheight{1.25}\smash{\begin{tabular}[t]{c}$C_{-1}=0$\end{tabular}}}}% 60 | \put(0,0){\includegraphics[width=\unitlength,page=1]{morse-chain-complex-visualized-truncated.pdf}}% 61 | \end{picture}% 62 | \endgroup% 63 | -------------------------------------------------------------------------------- /thesis/figures/morse-chain-complex-visualized.pdf: -------------------------------------------------------------------------------- https://raw.githubusercontent.com/gillescastel/masterthesis/16b33d4121a8958e624bb0c9157151a63311b119/thesis/figures/morse-chain-complex-visualized.pdf -------------------------------------------------------------------------------- /thesis/figures/morse-chart-flow-lines.pdf: -------------------------------------------------------------------------------- https://raw.githubusercontent.com/gillescastel/masterthesis/16b33d4121a8958e624bb0c9157151a63311b119/thesis/figures/morse-chart-flow-lines.pdf -------------------------------------------------------------------------------- /thesis/figures/morse-chart-flow-lines.pdf_tex: -------------------------------------------------------------------------------- 1 | %% Creator: Inkscape inkscape 0.92.4, www.inkscape.org 2 | %% PDF/EPS/PS + LaTeX output extension by Johan Engelen, 2010 3 | %% Accompanies image file 'morse-chart-flow-lines.pdf' (pdf, eps, ps) 4 | %% 5 | %% To include the image in your LaTeX document, write 6 | %% \input{.pdf_tex} 7 | %% instead of 8 | %% \includegraphics{.pdf} 9 | %% To scale the image, write 10 | %% \def\svgwidth{} 11 | %% \input{.pdf_tex} 12 | %% instead of 13 | %% \includegraphics[width=]{.pdf} 14 | %% 15 | %% Images with a different path to the parent latex file can 16 | %% be accessed with the `import' package (which may need to be 17 | %% installed) using 18 | %% \usepackage{import} 19 | %% in the preamble, and then including the image with 20 | %% \import{}{.pdf_tex} 21 | %% Alternatively, one can specify 22 | %% \graphicspath{{/}} 23 | %% 24 | %% For more information, please see info/svg-inkscape on CTAN: 25 | %% http://tug.ctan.org/tex-archive/info/svg-inkscape 26 | %% 27 | \begingroup% 28 | \makeatletter% 29 | \providecommand\color[2][]{% 30 | \errmessage{(Inkscape) Color is used for the text in Inkscape, but the package 'color.sty' is not loaded}% 31 | \renewcommand\color[2][]{}% 32 | }% 33 | \providecommand\transparent[1]{% 34 | \errmessage{(Inkscape) Transparency is used (non-zero) for the text in Inkscape, but the package 'transparent.sty' is not loaded}% 35 | \renewcommand\transparent[1]{}% 36 | }% 37 | \providecommand\rotatebox[2]{#2}% 38 | \newcommand*\fsize{\dimexpr\f@size pt\relax}% 39 | \newcommand*\lineheight[1]{\fontsize{\fsize}{#1\fsize}\selectfont}% 40 | \ifx\svgwidth\undefined% 41 | \setlength{\unitlength}{217.24309005bp}% 42 | \ifx\svgscale\undefined% 43 | \relax% 44 | \else% 45 | \setlength{\unitlength}{\unitlength * \real{\svgscale}}% 46 | \fi% 47 | \else% 48 | \setlength{\unitlength}{\svgwidth}% 49 | \fi% 50 | \global\let\svgwidth\undefined% 51 | \global\let\svgscale\undefined% 52 | \makeatother% 53 | \begin{picture}(1,0.85070889)% 54 | \lineheight{1}% 55 | \setlength\tabcolsep{0pt}% 56 | \put(0,0){\includegraphics[width=\unitlength,page=1]{morse-chart-flow-lines.pdf}}% 57 | \put(0.72867386,0.30116087){\color[rgb]{0,0,0}\makebox(0,0)[lt]{\lineheight{1.25}\smash{\begin{tabular}[t]{l}$x_1, \ldots, x_k$\end{tabular}}}}% 58 | \put(0.37372163,0.81895856){\color[rgb]{0,0,0}\makebox(0,0)[lt]{\lineheight{1.25}\smash{\begin{tabular}[t]{l}$x_{k+1}, \ldots, x_{n}$\end{tabular}}}}% 59 | \put(0.69958507,0.60967332){\color[rgb]{0,0,0}\makebox(0,0)[lt]{\lineheight{1.25}\smash{\begin{tabular}[t]{l}$f(p) = 0$\end{tabular}}}}% 60 | \put(0.74330676,0.5284467){\color[rgb]{0,0,0}\makebox(0,0)[lt]{\lineheight{1.25}\smash{\begin{tabular}[t]{l}$f(p) = -\epsilon$\end{tabular}}}}% 61 | \put(0.62077772,0.69578724){\color[rgb]{0,0,0}\makebox(0,0)[lt]{\lineheight{1.25}\smash{\begin{tabular}[t]{l}$f(p) = \epsilon$\end{tabular}}}}% 62 | \put(0,0){\includegraphics[width=\unitlength,page=2]{morse-chart-flow-lines.pdf}}% 63 | \end{picture}% 64 | \endgroup% 65 | -------------------------------------------------------------------------------- /thesis/figures/morse-chart-zoomed-in.pdf: -------------------------------------------------------------------------------- https://raw.githubusercontent.com/gillescastel/masterthesis/16b33d4121a8958e624bb0c9157151a63311b119/thesis/figures/morse-chart-zoomed-in.pdf -------------------------------------------------------------------------------- /thesis/figures/morse-chart-zoomed-in.pdf_tex: -------------------------------------------------------------------------------- 1 | %% Creator: Inkscape inkscape 0.92.4, www.inkscape.org 2 | %% PDF/EPS/PS + LaTeX output extension by Johan Engelen, 2010 3 | %% Accompanies image file 'morse-chart-zoomed-in.pdf' (pdf, eps, ps) 4 | %% 5 | %% To include the image in your LaTeX document, write 6 | %% \input{.pdf_tex} 7 | %% instead of 8 | %% \includegraphics{.pdf} 9 | %% To scale the image, write 10 | %% \def\svgwidth{} 11 | %% \input{.pdf_tex} 12 | %% instead of 13 | %% \includegraphics[width=]{.pdf} 14 | %% 15 | %% Images with a different path to the parent latex file can 16 | %% be accessed with the `import' package (which may need to be 17 | %% installed) using 18 | %% \usepackage{import} 19 | %% in the preamble, and then including the image with 20 | %% \import{}{.pdf_tex} 21 | %% Alternatively, one can specify 22 | %% \graphicspath{{/}} 23 | %% 24 | %% For more information, please see info/svg-inkscape on CTAN: 25 | %% http://tug.ctan.org/tex-archive/info/svg-inkscape 26 | %% 27 | \begingroup% 28 | \makeatletter% 29 | \providecommand\color[2][]{% 30 | \errmessage{(Inkscape) Color is used for the text in Inkscape, but the package 'color.sty' is not loaded}% 31 | \renewcommand\color[2][]{}% 32 | }% 33 | \providecommand\transparent[1]{% 34 | \errmessage{(Inkscape) Transparency is used (non-zero) for the text in Inkscape, but the package 'transparent.sty' is not loaded}% 35 | \renewcommand\transparent[1]{}% 36 | }% 37 | \providecommand\rotatebox[2]{#2}% 38 | \newcommand*\fsize{\dimexpr\f@size pt\relax}% 39 | \newcommand*\lineheight[1]{\fontsize{\fsize}{#1\fsize}\selectfont}% 40 | \ifx\svgwidth\undefined% 41 | \setlength{\unitlength}{360.40945699bp}% 42 | \ifx\svgscale\undefined% 43 | \relax% 44 | \else% 45 | \setlength{\unitlength}{\unitlength * \real{\svgscale}}% 46 | \fi% 47 | \else% 48 | \setlength{\unitlength}{\svgwidth}% 49 | \fi% 50 | \global\let\svgwidth\undefined% 51 | \global\let\svgscale\undefined% 52 | \makeatother% 53 | \begin{picture}(1,0.93721787)% 54 | \lineheight{1}% 55 | \setlength\tabcolsep{0pt}% 56 | \put(0,0){\includegraphics[width=\unitlength,page=1]{morse-chart-zoomed-in.pdf}}% 57 | \put(0.86674901,0.54298909){\color[rgb]{0,0,0}\makebox(0,0)[lt]{\lineheight{1.25}\smash{\begin{tabular}[t]{l}$f(\epsilon)$\end{tabular}}}}% 58 | \put(0.86674901,0.24555104){\color[rgb]{0,0,0}\makebox(0,0)[lt]{\lineheight{1.25}\smash{\begin{tabular}[t]{l}$f(-\epsilon)$\end{tabular}}}}% 59 | \put(0,0){\includegraphics[width=\unitlength,page=2]{morse-chart-zoomed-in.pdf}}% 60 | \end{picture}% 61 | \endgroup% 62 | -------------------------------------------------------------------------------- /thesis/figures/morse-chart.pdf: -------------------------------------------------------------------------------- https://raw.githubusercontent.com/gillescastel/masterthesis/16b33d4121a8958e624bb0c9157151a63311b119/thesis/figures/morse-chart.pdf -------------------------------------------------------------------------------- /thesis/figures/morse-complex-is-a-complex-idea-of-proof.pdf: -------------------------------------------------------------------------------- https://raw.githubusercontent.com/gillescastel/masterthesis/16b33d4121a8958e624bb0c9157151a63311b119/thesis/figures/morse-complex-is-a-complex-idea-of-proof.pdf -------------------------------------------------------------------------------- /thesis/figures/morse-function-sphere-example.pdf: -------------------------------------------------------------------------------- https://raw.githubusercontent.com/gillescastel/masterthesis/16b33d4121a8958e624bb0c9157151a63311b119/thesis/figures/morse-function-sphere-example.pdf -------------------------------------------------------------------------------- /thesis/figures/morse-homology-definition-of-topology.pdf: -------------------------------------------------------------------------------- https://raw.githubusercontent.com/gillescastel/masterthesis/16b33d4121a8958e624bb0c9157151a63311b119/thesis/figures/morse-homology-definition-of-topology.pdf -------------------------------------------------------------------------------- /thesis/figures/morse-homology-independence-cilinder.pdf: -------------------------------------------------------------------------------- https://raw.githubusercontent.com/gillescastel/masterthesis/16b33d4121a8958e624bb0c9157151a63311b119/thesis/figures/morse-homology-independence-cilinder.pdf -------------------------------------------------------------------------------- /thesis/figures/morse-homology-independence-cilinder.pdf_tex: -------------------------------------------------------------------------------- 1 | %% Creator: Inkscape inkscape 0.92.4, www.inkscape.org 2 | %% PDF/EPS/PS + LaTeX output extension by Johan Engelen, 2010 3 | %% Accompanies image file 'morse-homology-independence-cilinder.pdf' (pdf, eps, ps) 4 | %% 5 | %% To include the image in your LaTeX document, write 6 | %% \input{.pdf_tex} 7 | %% instead of 8 | %% \includegraphics{.pdf} 9 | %% To scale the image, write 10 | %% \def\svgwidth{} 11 | %% \input{.pdf_tex} 12 | %% instead of 13 | %% \includegraphics[width=]{.pdf} 14 | %% 15 | %% Images with a different path to the parent latex file can 16 | %% be accessed with the `import' package (which may need to be 17 | %% installed) using 18 | %% \usepackage{import} 19 | %% in the preamble, and then including the image with 20 | %% \import{}{.pdf_tex} 21 | %% Alternatively, one can specify 22 | %% \graphicspath{{/}} 23 | %% 24 | %% For more information, please see info/svg-inkscape on CTAN: 25 | %% http://tug.ctan.org/tex-archive/info/svg-inkscape 26 | %% 27 | \begingroup% 28 | \makeatletter% 29 | \providecommand\color[2][]{% 30 | \errmessage{(Inkscape) Color is used for the text in Inkscape, but the package 'color.sty' is not loaded}% 31 | \renewcommand\color[2][]{}% 32 | }% 33 | \providecommand\transparent[1]{% 34 | \errmessage{(Inkscape) Transparency is used (non-zero) for the text in Inkscape, but the package 'transparent.sty' is not loaded}% 35 | \renewcommand\transparent[1]{}% 36 | }% 37 | \providecommand\rotatebox[2]{#2}% 38 | \newcommand*\fsize{\dimexpr\f@size pt\relax}% 39 | \newcommand*\lineheight[1]{\fontsize{\fsize}{#1\fsize}\selectfont}% 40 | \ifx\svgwidth\undefined% 41 | \setlength{\unitlength}{201.97259137bp}% 42 | \ifx\svgscale\undefined% 43 | \relax% 44 | \else% 45 | \setlength{\unitlength}{\unitlength * \real{\svgscale}}% 46 | \fi% 47 | \else% 48 | \setlength{\unitlength}{\svgwidth}% 49 | \fi% 50 | \global\let\svgwidth\undefined% 51 | \global\let\svgscale\undefined% 52 | \makeatother% 53 | \begin{picture}(1,0.7437895)% 54 | \lineheight{1}% 55 | \setlength\tabcolsep{0pt}% 56 | \put(0,0){\includegraphics[width=\unitlength,page=1]{morse-homology-independence-cilinder.pdf}}% 57 | \put(0.89477761,0.00382481){\color[rgb]{0,0,0}\makebox(0,0)[lt]{\lineheight{1.25}\smash{\begin{tabular}[t]{l}$s$\end{tabular}}}}% 58 | \put(0,0){\includegraphics[width=\unitlength,page=2]{morse-homology-independence-cilinder.pdf}}% 59 | \put(-0.00204235,0.40931748){\color[rgb]{0,0,0}\makebox(0,0)[lt]{\lineheight{1.25}\smash{\begin{tabular}[t]{l}$0$\end{tabular}}}}% 60 | \put(0.74435987,0.01218539){\color[rgb]{0,0,0}\makebox(0,0)[lt]{\lineheight{1.25}\smash{\begin{tabular}[t]{l}$1$\end{tabular}}}}% 61 | \end{picture}% 62 | \endgroup% 63 | -------------------------------------------------------------------------------- /thesis/figures/morse-homology-independence-g-function.pdf: -------------------------------------------------------------------------------- https://raw.githubusercontent.com/gillescastel/masterthesis/16b33d4121a8958e624bb0c9157151a63311b119/thesis/figures/morse-homology-independence-g-function.pdf -------------------------------------------------------------------------------- /thesis/figures/morse-homology-independence-partial-squared-zero-bis.pdf: -------------------------------------------------------------------------------- https://raw.githubusercontent.com/gillescastel/masterthesis/16b33d4121a8958e624bb0c9157151a63311b119/thesis/figures/morse-homology-independence-partial-squared-zero-bis.pdf -------------------------------------------------------------------------------- /thesis/figures/morse-homology-independence-partial-squared-zero.pdf: -------------------------------------------------------------------------------- https://raw.githubusercontent.com/gillescastel/masterthesis/16b33d4121a8958e624bb0c9157151a63311b119/thesis/figures/morse-homology-independence-partial-squared-zero.pdf -------------------------------------------------------------------------------- /thesis/figures/morse-homology-independence-tube.pdf: -------------------------------------------------------------------------------- https://raw.githubusercontent.com/gillescastel/masterthesis/16b33d4121a8958e624bb0c9157151a63311b119/thesis/figures/morse-homology-independence-tube.pdf -------------------------------------------------------------------------------- /thesis/figures/morse-homology-independence-tube.pdf_tex: -------------------------------------------------------------------------------- 1 | %% Creator: Inkscape inkscape 0.92.4, www.inkscape.org 2 | %% PDF/EPS/PS + LaTeX output extension by Johan Engelen, 2010 3 | %% Accompanies image file 'morse-homology-independence-tube.pdf' (pdf, eps, ps) 4 | %% 5 | %% To include the image in your LaTeX document, write 6 | %% \input{.pdf_tex} 7 | %% instead of 8 | %% \includegraphics{.pdf} 9 | %% To scale the image, write 10 | %% \def\svgwidth{} 11 | %% \input{.pdf_tex} 12 | %% instead of 13 | %% \includegraphics[width=]{.pdf} 14 | %% 15 | %% Images with a different path to the parent latex file can 16 | %% be accessed with the `import' package (which may need to be 17 | %% installed) using 18 | %% \usepackage{import} 19 | %% in the preamble, and then including the image with 20 | %% \import{}{.pdf_tex} 21 | %% Alternatively, one can specify 22 | %% \graphicspath{{/}} 23 | %% 24 | %% For more information, please see info/svg-inkscape on CTAN: 25 | %% http://tug.ctan.org/tex-archive/info/svg-inkscape 26 | %% 27 | \begingroup% 28 | \makeatletter% 29 | \providecommand\color[2][]{% 30 | \errmessage{(Inkscape) Color is used for the text in Inkscape, but the package 'color.sty' is not loaded}% 31 | \renewcommand\color[2][]{}% 32 | }% 33 | \providecommand\transparent[1]{% 34 | \errmessage{(Inkscape) Transparency is used (non-zero) for the text in Inkscape, but the package 'transparent.sty' is not loaded}% 35 | \renewcommand\transparent[1]{}% 36 | }% 37 | \providecommand\rotatebox[2]{#2}% 38 | \newcommand*\fsize{\dimexpr\f@size pt\relax}% 39 | \newcommand*\lineheight[1]{\fontsize{\fsize}{#1\fsize}\selectfont}% 40 | \ifx\svgwidth\undefined% 41 | \setlength{\unitlength}{302.18163678bp}% 42 | \ifx\svgscale\undefined% 43 | \relax% 44 | \else% 45 | \setlength{\unitlength}{\unitlength * \real{\svgscale}}% 46 | \fi% 47 | \else% 48 | \setlength{\unitlength}{\svgwidth}% 49 | \fi% 50 | \global\let\svgwidth\undefined% 51 | \global\let\svgscale\undefined% 52 | \makeatother% 53 | \begin{picture}(1,1.08711653)% 54 | \lineheight{1}% 55 | \setlength\tabcolsep{0pt}% 56 | \put(0,0){\includegraphics[width=\unitlength,page=1]{morse-homology-independence-tube.pdf}}% 57 | \put(0.9122075,0.01566209){\color[rgb]{0,0,0}\makebox(0,0)[lt]{\lineheight{1.25}\smash{\begin{tabular}[t]{l}$s$\end{tabular}}}}% 58 | \put(0,0){\includegraphics[width=\unitlength,page=2]{morse-homology-independence-tube.pdf}}% 59 | \put(0.13598612,0.33525268){\color[rgb]{0,0,0}\makebox(0,0)[lt]{\lineheight{1.25}\smash{\begin{tabular}[t]{l}$0$\end{tabular}}}}% 60 | \put(0.63361946,0.06732095){\color[rgb]{0,0,0}\makebox(0,0)[lt]{\lineheight{1.25}\smash{\begin{tabular}[t]{l}$1$\end{tabular}}}}% 61 | \put(0,0){\includegraphics[width=\unitlength,page=3]{morse-homology-independence-tube.pdf}}% 62 | \end{picture}% 63 | \endgroup% 64 | -------------------------------------------------------------------------------- /thesis/figures/morse-homology-independence-two-dimensional-slide-three-d.pdf: -------------------------------------------------------------------------------- https://raw.githubusercontent.com/gillescastel/masterthesis/16b33d4121a8958e624bb0c9157151a63311b119/thesis/figures/morse-homology-independence-two-dimensional-slide-three-d.pdf -------------------------------------------------------------------------------- /thesis/figures/morse-homology-independence-two-dimensional-slide.pdf: -------------------------------------------------------------------------------- https://raw.githubusercontent.com/gillescastel/masterthesis/16b33d4121a8958e624bb0c9157151a63311b119/thesis/figures/morse-homology-independence-two-dimensional-slide.pdf -------------------------------------------------------------------------------- /thesis/figures/morse-homology-is-singular-homology-defining-map-a.pdf: -------------------------------------------------------------------------------- https://raw.githubusercontent.com/gillescastel/masterthesis/16b33d4121a8958e624bb0c9157151a63311b119/thesis/figures/morse-homology-is-singular-homology-defining-map-a.pdf -------------------------------------------------------------------------------- /thesis/figures/morse-homology-is-singular-homology-defining-map-a.pdf_tex: -------------------------------------------------------------------------------- 1 | %% Creator: Inkscape inkscape 0.92.4, www.inkscape.org 2 | %% PDF/EPS/PS + LaTeX output extension by Johan Engelen, 2010 3 | %% Accompanies image file 'morse-homology-is-singular-homology-defining-map-a.pdf' (pdf, eps, ps) 4 | %% 5 | %% To include the image in your LaTeX document, write 6 | %% \input{.pdf_tex} 7 | %% instead of 8 | %% \includegraphics{.pdf} 9 | %% To scale the image, write 10 | %% \def\svgwidth{} 11 | %% \input{.pdf_tex} 12 | %% instead of 13 | %% \includegraphics[width=]{.pdf} 14 | %% 15 | %% Images with a different path to the parent latex file can 16 | %% be accessed with the `import' package (which may need to be 17 | %% installed) using 18 | %% \usepackage{import} 19 | %% in the preamble, and then including the image with 20 | %% \import{}{.pdf_tex} 21 | %% Alternatively, one can specify 22 | %% \graphicspath{{/}} 23 | %% 24 | %% For more information, please see info/svg-inkscape on CTAN: 25 | %% http://tug.ctan.org/tex-archive/info/svg-inkscape 26 | %% 27 | \begingroup% 28 | \makeatletter% 29 | \providecommand\color[2][]{% 30 | \errmessage{(Inkscape) Color is used for the text in Inkscape, but the package 'color.sty' is not loaded}% 31 | \renewcommand\color[2][]{}% 32 | }% 33 | \providecommand\transparent[1]{% 34 | \errmessage{(Inkscape) Transparency is used (non-zero) for the text in Inkscape, but the package 'transparent.sty' is not loaded}% 35 | \renewcommand\transparent[1]{}% 36 | }% 37 | \providecommand\rotatebox[2]{#2}% 38 | \newcommand*\fsize{\dimexpr\f@size pt\relax}% 39 | \newcommand*\lineheight[1]{\fontsize{\fsize}{#1\fsize}\selectfont}% 40 | \ifx\svgwidth\undefined% 41 | \setlength{\unitlength}{241.75471268bp}% 42 | \ifx\svgscale\undefined% 43 | \relax% 44 | \else% 45 | \setlength{\unitlength}{\unitlength * \real{\svgscale}}% 46 | \fi% 47 | \else% 48 | \setlength{\unitlength}{\svgwidth}% 49 | \fi% 50 | \global\let\svgwidth\undefined% 51 | \global\let\svgscale\undefined% 52 | \makeatother% 53 | \begin{picture}(1,0.55468219)% 54 | \lineheight{1}% 55 | \setlength\tabcolsep{0pt}% 56 | \put(0,0){\includegraphics[width=\unitlength,page=1]{morse-homology-is-singular-homology-defining-map-a.pdf}}% 57 | \end{picture}% 58 | \endgroup% 59 | -------------------------------------------------------------------------------- /thesis/figures/morse-homology-other-sphere-differential.pdf: -------------------------------------------------------------------------------- https://raw.githubusercontent.com/gillescastel/masterthesis/16b33d4121a8958e624bb0c9157151a63311b119/thesis/figures/morse-homology-other-sphere-differential.pdf -------------------------------------------------------------------------------- /thesis/figures/morse-homology-three-torus-trajectories.pdf: -------------------------------------------------------------------------------- https://raw.githubusercontent.com/gillescastel/masterthesis/16b33d4121a8958e624bb0c9157151a63311b119/thesis/figures/morse-homology-three-torus-trajectories.pdf -------------------------------------------------------------------------------- /thesis/figures/morse-homology-three-torus-trajectories.pdf_tex: -------------------------------------------------------------------------------- 1 | %% Creator: Inkscape inkscape 0.92.4, www.inkscape.org 2 | %% PDF/EPS/PS + LaTeX output extension by Johan Engelen, 2010 3 | %% Accompanies image file 'morse-homology-three-torus-trajectories.pdf' (pdf, eps, ps) 4 | %% 5 | %% To include the image in your LaTeX document, write 6 | %% \input{.pdf_tex} 7 | %% instead of 8 | %% \includegraphics{.pdf} 9 | %% To scale the image, write 10 | %% \def\svgwidth{} 11 | %% \input{.pdf_tex} 12 | %% instead of 13 | %% \includegraphics[width=]{.pdf} 14 | %% 15 | %% Images with a different path to the parent latex file can 16 | %% be accessed with the `import' package (which may need to be 17 | %% installed) using 18 | %% \usepackage{import} 19 | %% in the preamble, and then including the image with 20 | %% \import{}{.pdf_tex} 21 | %% Alternatively, one can specify 22 | %% \graphicspath{{/}} 23 | %% 24 | %% For more information, please see info/svg-inkscape on CTAN: 25 | %% http://tug.ctan.org/tex-archive/info/svg-inkscape 26 | %% 27 | \begingroup% 28 | \makeatletter% 29 | \providecommand\color[2][]{% 30 | \errmessage{(Inkscape) Color is used for the text in Inkscape, but the package 'color.sty' is not loaded}% 31 | \renewcommand\color[2][]{}% 32 | }% 33 | \providecommand\transparent[1]{% 34 | \errmessage{(Inkscape) Transparency is used (non-zero) for the text in Inkscape, but the package 'transparent.sty' is not loaded}% 35 | \renewcommand\transparent[1]{}% 36 | }% 37 | \providecommand\rotatebox[2]{#2}% 38 | \newcommand*\fsize{\dimexpr\f@size pt\relax}% 39 | \newcommand*\lineheight[1]{\fontsize{\fsize}{#1\fsize}\selectfont}% 40 | \ifx\svgwidth\undefined% 41 | \setlength{\unitlength}{281.59857803bp}% 42 | \ifx\svgscale\undefined% 43 | \relax% 44 | \else% 45 | \setlength{\unitlength}{\unitlength * \real{\svgscale}}% 46 | \fi% 47 | \else% 48 | \setlength{\unitlength}{\svgwidth}% 49 | \fi% 50 | \global\let\svgwidth\undefined% 51 | \global\let\svgscale\undefined% 52 | \makeatother% 53 | \begin{picture}(1,0.68560604)% 54 | \lineheight{1}% 55 | \setlength\tabcolsep{0pt}% 56 | \put(0,0){\includegraphics[width=\unitlength,page=1]{morse-homology-three-torus-trajectories.pdf}}% 57 | \end{picture}% 58 | \endgroup% 59 | -------------------------------------------------------------------------------- /thesis/figures/non-example-of-morse-function.pdf: -------------------------------------------------------------------------------- https://raw.githubusercontent.com/gillescastel/masterthesis/16b33d4121a8958e624bb0c9157151a63311b119/thesis/figures/non-example-of-morse-function.pdf -------------------------------------------------------------------------------- /thesis/figures/non-example-of-morse-function.pdf_tex: -------------------------------------------------------------------------------- 1 | %% Creator: Inkscape inkscape 0.92.4, www.inkscape.org 2 | %% PDF/EPS/PS + LaTeX output extension by Johan Engelen, 2010 3 | %% Accompanies image file 'non-example-of-morse-function.pdf' (pdf, eps, ps) 4 | %% 5 | %% To include the image in your LaTeX document, write 6 | %% \input{.pdf_tex} 7 | %% instead of 8 | %% \includegraphics{.pdf} 9 | %% To scale the image, write 10 | %% \def\svgwidth{} 11 | %% \input{.pdf_tex} 12 | %% instead of 13 | %% \includegraphics[width=]{.pdf} 14 | %% 15 | %% Images with a different path to the parent latex file can 16 | %% be accessed with the `import' package (which may need to be 17 | %% installed) using 18 | %% \usepackage{import} 19 | %% in the preamble, and then including the image with 20 | %% \import{}{.pdf_tex} 21 | %% Alternatively, one can specify 22 | %% \graphicspath{{/}} 23 | %% 24 | %% For more information, please see info/svg-inkscape on CTAN: 25 | %% http://tug.ctan.org/tex-archive/info/svg-inkscape 26 | %% 27 | \begingroup% 28 | \makeatletter% 29 | \providecommand\color[2][]{% 30 | \errmessage{(Inkscape) Color is used for the text in Inkscape, but the package 'color.sty' is not loaded}% 31 | \renewcommand\color[2][]{}% 32 | }% 33 | \providecommand\transparent[1]{% 34 | \errmessage{(Inkscape) Transparency is used (non-zero) for the text in Inkscape, but the package 'transparent.sty' is not loaded}% 35 | \renewcommand\transparent[1]{}% 36 | }% 37 | \providecommand\rotatebox[2]{#2}% 38 | \newcommand*\fsize{\dimexpr\f@size pt\relax}% 39 | \newcommand*\lineheight[1]{\fontsize{\fsize}{#1\fsize}\selectfont}% 40 | \ifx\svgwidth\undefined% 41 | \setlength{\unitlength}{294.79030339bp}% 42 | \ifx\svgscale\undefined% 43 | \relax% 44 | \else% 45 | \setlength{\unitlength}{\unitlength * \real{\svgscale}}% 46 | \fi% 47 | \else% 48 | \setlength{\unitlength}{\svgwidth}% 49 | \fi% 50 | \global\let\svgwidth\undefined% 51 | \global\let\svgscale\undefined% 52 | \makeatother% 53 | \begin{picture}(1,0.47293325)% 54 | \lineheight{1}% 55 | \setlength\tabcolsep{0pt}% 56 | \put(0,0){\includegraphics[width=\unitlength,page=1]{non-example-of-morse-function.pdf}}% 57 | \put(0.60143704,0.40475595){\color[rgb]{0,0,0}\makebox(0,0)[lt]{\lineheight{1.25}\smash{\begin{tabular}[t]{l}$(x, y) \mapsto x^2$\end{tabular}}}}% 58 | \put(0,0){\includegraphics[width=\unitlength,page=2]{non-example-of-morse-function.pdf}}% 59 | \end{picture}% 60 | \endgroup% 61 | -------------------------------------------------------------------------------- /thesis/figures/non-examples-of-morse-functions.pdf: -------------------------------------------------------------------------------- https://raw.githubusercontent.com/gillescastel/masterthesis/16b33d4121a8958e624bb0c9157151a63311b119/thesis/figures/non-examples-of-morse-functions.pdf -------------------------------------------------------------------------------- /thesis/figures/non-examples-of-morse-functions.pdf_tex: -------------------------------------------------------------------------------- 1 | %% Creator: Inkscape inkscape 0.92.4, www.inkscape.org 2 | %% PDF/EPS/PS + LaTeX output extension by Johan Engelen, 2010 3 | %% Accompanies image file 'non-examples-of-morse-functions.pdf' (pdf, eps, ps) 4 | %% 5 | %% To include the image in your LaTeX document, write 6 | %% \input{.pdf_tex} 7 | %% instead of 8 | %% \includegraphics{.pdf} 9 | %% To scale the image, write 10 | %% \def\svgwidth{} 11 | %% \input{.pdf_tex} 12 | %% instead of 13 | %% \includegraphics[width=]{.pdf} 14 | %% 15 | %% Images with a different path to the parent latex file can 16 | %% be accessed with the `import' package (which may need to be 17 | %% installed) using 18 | %% \usepackage{import} 19 | %% in the preamble, and then including the image with 20 | %% \import{}{.pdf_tex} 21 | %% Alternatively, one can specify 22 | %% \graphicspath{{/}} 23 | %% 24 | %% For more information, please see info/svg-inkscape on CTAN: 25 | %% http://tug.ctan.org/tex-archive/info/svg-inkscape 26 | %% 27 | \begingroup% 28 | \makeatletter% 29 | \providecommand\color[2][]{% 30 | \errmessage{(Inkscape) Color is used for the text in Inkscape, but the package 'color.sty' is not loaded}% 31 | \renewcommand\color[2][]{}% 32 | }% 33 | \providecommand\transparent[1]{% 34 | \errmessage{(Inkscape) Transparency is used (non-zero) for the text in Inkscape, but the package 'transparent.sty' is not loaded}% 35 | \renewcommand\transparent[1]{}% 36 | }% 37 | \providecommand\rotatebox[2]{#2}% 38 | \newcommand*\fsize{\dimexpr\f@size pt\relax}% 39 | \newcommand*\lineheight[1]{\fontsize{\fsize}{#1\fsize}\selectfont}% 40 | \ifx\svgwidth\undefined% 41 | \setlength{\unitlength}{277.44269664bp}% 42 | \ifx\svgscale\undefined% 43 | \relax% 44 | \else% 45 | \setlength{\unitlength}{\unitlength * \real{\svgscale}}% 46 | \fi% 47 | \else% 48 | \setlength{\unitlength}{\svgwidth}% 49 | \fi% 50 | \global\let\svgwidth\undefined% 51 | \global\let\svgscale\undefined% 52 | \makeatother% 53 | \begin{picture}(1,0.84368301)% 54 | \lineheight{1}% 55 | \setlength\tabcolsep{0pt}% 56 | \put(0,0){\includegraphics[width=\unitlength,page=1]{non-examples-of-morse-functions.pdf}}% 57 | \put(0.76121042,0.77419231){\color[rgb]{0,0,0}\makebox(0,0)[lt]{\lineheight{1.25}\smash{\begin{tabular}[t]{l}$x^3$\end{tabular}}}}% 58 | \put(0,0){\includegraphics[width=\unitlength,page=2]{non-examples-of-morse-functions.pdf}}% 59 | \put(0.72222846,0.30822668){\color[rgb]{0,0,0}\makebox(0,0)[lt]{\lineheight{1.25}\smash{\begin{tabular}[t]{l}$x^3 + tx$\end{tabular}}}}% 60 | \put(0,0){\includegraphics[width=\unitlength,page=3]{non-examples-of-morse-functions.pdf}}% 61 | \end{picture}% 62 | \endgroup% 63 | -------------------------------------------------------------------------------- /thesis/figures/one-dimensional-handle-decomposition-examples.pdf: -------------------------------------------------------------------------------- https://raw.githubusercontent.com/gillescastel/masterthesis/16b33d4121a8958e624bb0c9157151a63311b119/thesis/figures/one-dimensional-handle-decomposition-examples.pdf -------------------------------------------------------------------------------- /thesis/figures/one-dimensional-reduction.pdf: -------------------------------------------------------------------------------- https://raw.githubusercontent.com/gillescastel/masterthesis/16b33d4121a8958e624bb0c9157151a63311b119/thesis/figures/one-dimensional-reduction.pdf -------------------------------------------------------------------------------- /thesis/figures/orientation-example.pdf: -------------------------------------------------------------------------------- https://raw.githubusercontent.com/gillescastel/masterthesis/16b33d4121a8958e624bb0c9157151a63311b119/thesis/figures/orientation-example.pdf -------------------------------------------------------------------------------- /thesis/figures/other-sphere-and-normal-sphere-morse-complex.pdf: -------------------------------------------------------------------------------- https://raw.githubusercontent.com/gillescastel/masterthesis/16b33d4121a8958e624bb0c9157151a63311b119/thesis/figures/other-sphere-and-normal-sphere-morse-complex.pdf -------------------------------------------------------------------------------- /thesis/figures/other-sphere-cancelation-of-critical-points.pdf: -------------------------------------------------------------------------------- https://raw.githubusercontent.com/gillescastel/masterthesis/16b33d4121a8958e624bb0c9157151a63311b119/thesis/figures/other-sphere-cancelation-of-critical-points.pdf -------------------------------------------------------------------------------- /thesis/figures/other-sphere-cancelation-of-critical-points.pdf_tex: -------------------------------------------------------------------------------- 1 | %% Creator: Inkscape inkscape 0.92.4, www.inkscape.org 2 | %% PDF/EPS/PS + LaTeX output extension by Johan Engelen, 2010 3 | %% Accompanies image file 'other-sphere-cancelation-of-critical-points.pdf' (pdf, eps, ps) 4 | %% 5 | %% To include the image in your LaTeX document, write 6 | %% \input{.pdf_tex} 7 | %% instead of 8 | %% \includegraphics{.pdf} 9 | %% To scale the image, write 10 | %% \def\svgwidth{} 11 | %% \input{.pdf_tex} 12 | %% instead of 13 | %% \includegraphics[width=]{.pdf} 14 | %% 15 | %% Images with a different path to the parent latex file can 16 | %% be accessed with the `import' package (which may need to be 17 | %% installed) using 18 | %% \usepackage{import} 19 | %% in the preamble, and then including the image with 20 | %% \import{}{.pdf_tex} 21 | %% Alternatively, one can specify 22 | %% \graphicspath{{/}} 23 | %% 24 | %% For more information, please see info/svg-inkscape on CTAN: 25 | %% http://tug.ctan.org/tex-archive/info/svg-inkscape 26 | %% 27 | \begingroup% 28 | \makeatletter% 29 | \providecommand\color[2][]{% 30 | \errmessage{(Inkscape) Color is used for the text in Inkscape, but the package 'color.sty' is not loaded}% 31 | \renewcommand\color[2][]{}% 32 | }% 33 | \providecommand\transparent[1]{% 34 | \errmessage{(Inkscape) Transparency is used (non-zero) for the text in Inkscape, but the package 'transparent.sty' is not loaded}% 35 | \renewcommand\transparent[1]{}% 36 | }% 37 | \providecommand\rotatebox[2]{#2}% 38 | \newcommand*\fsize{\dimexpr\f@size pt\relax}% 39 | \newcommand*\lineheight[1]{\fontsize{\fsize}{#1\fsize}\selectfont}% 40 | \ifx\svgwidth\undefined% 41 | \setlength{\unitlength}{196.54339888bp}% 42 | \ifx\svgscale\undefined% 43 | \relax% 44 | \else% 45 | \setlength{\unitlength}{\unitlength * \real{\svgscale}}% 46 | \fi% 47 | \else% 48 | \setlength{\unitlength}{\svgwidth}% 49 | \fi% 50 | \global\let\svgwidth\undefined% 51 | \global\let\svgscale\undefined% 52 | \makeatother% 53 | \begin{picture}(1,0.79323708)% 54 | \lineheight{1}% 55 | \setlength\tabcolsep{0pt}% 56 | \put(0,0){\includegraphics[width=\unitlength,page=1]{other-sphere-cancelation-of-critical-points.pdf}}% 57 | \put(0.37262914,0.75224119){\color[rgb]{0,0,0}\makebox(0,0)[lt]{\lineheight{1.25}\smash{\begin{tabular}[t]{l}$c$\end{tabular}}}}% 58 | \put(0.64887726,0.61246277){\color[rgb]{0,0,0}\makebox(0,0)[lt]{\lineheight{1.25}\smash{\begin{tabular}[t]{l}$d$\end{tabular}}}}% 59 | \put(0,0){\includegraphics[width=\unitlength,page=2]{other-sphere-cancelation-of-critical-points.pdf}}% 60 | \put(0.48650871,0.48359234){\color[rgb]{0,0,0}\makebox(0,0)[lt]{\lineheight{1.25}\smash{\begin{tabular}[t]{l}$b$\end{tabular}}}}% 61 | \put(0,0){\includegraphics[width=\unitlength,page=3]{other-sphere-cancelation-of-critical-points.pdf}}% 62 | \put(0.53509112,-0.03144509){\color[rgb]{0,0,0}\makebox(0,0)[lt]{\lineheight{1.25}\smash{\begin{tabular}[t]{l}$a$\end{tabular}}}}% 63 | \end{picture}% 64 | \endgroup% 65 | -------------------------------------------------------------------------------- /thesis/figures/other-sphere-definition-of-mathcal-m.pdf: -------------------------------------------------------------------------------- https://raw.githubusercontent.com/gillescastel/masterthesis/16b33d4121a8958e624bb0c9157151a63311b119/thesis/figures/other-sphere-definition-of-mathcal-m.pdf -------------------------------------------------------------------------------- /thesis/figures/other-sphere-morse-complex-modules.pdf: -------------------------------------------------------------------------------- https://raw.githubusercontent.com/gillescastel/masterthesis/16b33d4121a8958e624bb0c9157151a63311b119/thesis/figures/other-sphere-morse-complex-modules.pdf -------------------------------------------------------------------------------- /thesis/figures/partial-squared-zero-space-compact.pdf: -------------------------------------------------------------------------------- https://raw.githubusercontent.com/gillescastel/masterthesis/16b33d4121a8958e624bb0c9157151a63311b119/thesis/figures/partial-squared-zero-space-compact.pdf -------------------------------------------------------------------------------- /thesis/figures/proof-e1-e2-e3-disconnect-case.pdf: -------------------------------------------------------------------------------- https://raw.githubusercontent.com/gillescastel/masterthesis/16b33d4121a8958e624bb0c9157151a63311b119/thesis/figures/proof-e1-e2-e3-disconnect-case.pdf -------------------------------------------------------------------------------- /thesis/figures/proof-e1-e2-e3-disconnect-case.pdf_tex: -------------------------------------------------------------------------------- 1 | %% Creator: Inkscape inkscape 0.92.4, www.inkscape.org 2 | %% PDF/EPS/PS + LaTeX output extension by Johan Engelen, 2010 3 | %% Accompanies image file 'proof-e1-e2-e3-disconnect-case.pdf' (pdf, eps, ps) 4 | %% 5 | %% To include the image in your LaTeX document, write 6 | %% \input{.pdf_tex} 7 | %% instead of 8 | %% \includegraphics{.pdf} 9 | %% To scale the image, write 10 | %% \def\svgwidth{} 11 | %% \input{.pdf_tex} 12 | %% instead of 13 | %% \includegraphics[width=]{.pdf} 14 | %% 15 | %% Images with a different path to the parent latex file can 16 | %% be accessed with the `import' package (which may need to be 17 | %% installed) using 18 | %% \usepackage{import} 19 | %% in the preamble, and then including the image with 20 | %% \import{}{.pdf_tex} 21 | %% Alternatively, one can specify 22 | %% \graphicspath{{/}} 23 | %% 24 | %% For more information, please see info/svg-inkscape on CTAN: 25 | %% http://tug.ctan.org/tex-archive/info/svg-inkscape 26 | %% 27 | \begingroup% 28 | \makeatletter% 29 | \providecommand\color[2][]{% 30 | \errmessage{(Inkscape) Color is used for the text in Inkscape, but the package 'color.sty' is not loaded}% 31 | \renewcommand\color[2][]{}% 32 | }% 33 | \providecommand\transparent[1]{% 34 | \errmessage{(Inkscape) Transparency is used (non-zero) for the text in Inkscape, but the package 'transparent.sty' is not loaded}% 35 | \renewcommand\transparent[1]{}% 36 | }% 37 | \providecommand\rotatebox[2]{#2}% 38 | \newcommand*\fsize{\dimexpr\f@size pt\relax}% 39 | \newcommand*\lineheight[1]{\fontsize{\fsize}{#1\fsize}\selectfont}% 40 | \ifx\svgwidth\undefined% 41 | \setlength{\unitlength}{307.02803484bp}% 42 | \ifx\svgscale\undefined% 43 | \relax% 44 | \else% 45 | \setlength{\unitlength}{\unitlength * \real{\svgscale}}% 46 | \fi% 47 | \else% 48 | \setlength{\unitlength}{\svgwidth}% 49 | \fi% 50 | \global\let\svgwidth\undefined% 51 | \global\let\svgscale\undefined% 52 | \makeatother% 53 | \begin{picture}(1,0.47210014)% 54 | \lineheight{1}% 55 | \setlength\tabcolsep{0pt}% 56 | \put(0,0){\includegraphics[width=\unitlength,page=1]{proof-e1-e2-e3-disconnect-case.pdf}}% 57 | \put(0.37789842,0.39205002){\color[rgb]{0,0,0}\makebox(0,0)[lt]{\lineheight{1.25}\smash{\begin{tabular}[t]{l}$V$\end{tabular}}}}% 58 | \put(0.01466225,0.39231966){\color[rgb]{0,0,0}\makebox(0,0)[lt]{\lineheight{1.25}\smash{\begin{tabular}[t]{l}$W$\end{tabular}}}}% 59 | \put(0.54911617,0.39231966){\color[rgb]{0,0,0}\makebox(0,0)[lt]{\lineheight{1.25}\smash{\begin{tabular}[t]{l}$W$\end{tabular}}}}% 60 | \put(0.50057488,0.00520311){\color[rgb]{0,0,0}\makebox(0,0)[t]{\lineheight{1.25}\smash{\begin{tabular}[t]{c}$M^{3/2} \setminus V \quad \cong \quad M^{1/2} \setminus (S^u(q_1) \cup S^u(q_2))$\end{tabular}}}}% 61 | \put(0,0){\includegraphics[width=\unitlength,page=2]{proof-e1-e2-e3-disconnect-case.pdf}}% 62 | \end{picture}% 63 | \endgroup% 64 | -------------------------------------------------------------------------------- /thesis/figures/proof-of-cobordism-without-critical-points.pdf: -------------------------------------------------------------------------------- https://raw.githubusercontent.com/gillescastel/masterthesis/16b33d4121a8958e624bb0c9157151a63311b119/thesis/figures/proof-of-cobordism-without-critical-points.pdf -------------------------------------------------------------------------------- /thesis/figures/proof-reordening-properties-of-g.pdf: -------------------------------------------------------------------------------- https://raw.githubusercontent.com/gillescastel/masterthesis/16b33d4121a8958e624bb0c9157151a63311b119/thesis/figures/proof-reordening-properties-of-g.pdf -------------------------------------------------------------------------------- /thesis/figures/rank-codimension.pdf: -------------------------------------------------------------------------------- https://raw.githubusercontent.com/gillescastel/masterthesis/16b33d4121a8958e624bb0c9157151a63311b119/thesis/figures/rank-codimension.pdf -------------------------------------------------------------------------------- /thesis/figures/reordening-theorem-milnor-h-cobordism.pdf: -------------------------------------------------------------------------------- https://raw.githubusercontent.com/gillescastel/masterthesis/16b33d4121a8958e624bb0c9157151a63311b119/thesis/figures/reordening-theorem-milnor-h-cobordism.pdf -------------------------------------------------------------------------------- /thesis/figures/ricci-flow.pdf: -------------------------------------------------------------------------------- https://raw.githubusercontent.com/gillescastel/masterthesis/16b33d4121a8958e624bb0c9157151a63311b119/thesis/figures/ricci-flow.pdf -------------------------------------------------------------------------------- /thesis/figures/ricci-flow.pdf_tex: -------------------------------------------------------------------------------- 1 | %% Creator: Inkscape inkscape 0.92.4, www.inkscape.org 2 | %% PDF/EPS/PS + LaTeX output extension by Johan Engelen, 2010 3 | %% Accompanies image file 'ricci-flow.pdf' (pdf, eps, ps) 4 | %% 5 | %% To include the image in your LaTeX document, write 6 | %% \input{.pdf_tex} 7 | %% instead of 8 | %% \includegraphics{.pdf} 9 | %% To scale the image, write 10 | %% \def\svgwidth{} 11 | %% \input{.pdf_tex} 12 | %% instead of 13 | %% \includegraphics[width=]{.pdf} 14 | %% 15 | %% Images with a different path to the parent latex file can 16 | %% be accessed with the `import' package (which may need to be 17 | %% installed) using 18 | %% \usepackage{import} 19 | %% in the preamble, and then including the image with 20 | %% \import{}{.pdf_tex} 21 | %% Alternatively, one can specify 22 | %% \graphicspath{{/}} 23 | %% 24 | %% For more information, please see info/svg-inkscape on CTAN: 25 | %% http://tug.ctan.org/tex-archive/info/svg-inkscape 26 | %% 27 | \begingroup% 28 | \makeatletter% 29 | \providecommand\color[2][]{% 30 | \errmessage{(Inkscape) Color is used for the text in Inkscape, but the package 'color.sty' is not loaded}% 31 | \renewcommand\color[2][]{}% 32 | }% 33 | \providecommand\transparent[1]{% 34 | \errmessage{(Inkscape) Transparency is used (non-zero) for the text in Inkscape, but the package 'transparent.sty' is not loaded}% 35 | \renewcommand\transparent[1]{}% 36 | }% 37 | \providecommand\rotatebox[2]{#2}% 38 | \newcommand*\fsize{\dimexpr\f@size pt\relax}% 39 | \newcommand*\lineheight[1]{\fontsize{\fsize}{#1\fsize}\selectfont}% 40 | \ifx\svgwidth\undefined% 41 | \setlength{\unitlength}{177.96884852bp}% 42 | \ifx\svgscale\undefined% 43 | \relax% 44 | \else% 45 | \setlength{\unitlength}{\unitlength * \real{\svgscale}}% 46 | \fi% 47 | \else% 48 | \setlength{\unitlength}{\svgwidth}% 49 | \fi% 50 | \global\let\svgwidth\undefined% 51 | \global\let\svgscale\undefined% 52 | \makeatother% 53 | \begin{picture}(1,0.94991398)% 54 | \lineheight{1}% 55 | \setlength\tabcolsep{0pt}% 56 | \put(0,0){\includegraphics[width=\unitlength,page=1]{ricci-flow.pdf}}% 57 | \put(0.21637175,0.06164129){\color[rgb]{0,0,0}\makebox(0,0)[lt]{\lineheight{1.25}\smash{\begin{tabular}[t]{l}$t$\end{tabular}}}}% 58 | \end{picture}% 59 | \endgroup% 60 | -------------------------------------------------------------------------------- /thesis/figures/second-cancellation-theorem-example.pdf: -------------------------------------------------------------------------------- https://raw.githubusercontent.com/gillescastel/masterthesis/16b33d4121a8958e624bb0c9157151a63311b119/thesis/figures/second-cancellation-theorem-example.pdf -------------------------------------------------------------------------------- /thesis/figures/second-cancellation-theorem-setup.pdf: -------------------------------------------------------------------------------- https://raw.githubusercontent.com/gillescastel/masterthesis/16b33d4121a8958e624bb0c9157151a63311b119/thesis/figures/second-cancellation-theorem-setup.pdf -------------------------------------------------------------------------------- /thesis/figures/self-indexing-morse-function-torus-tilted.pdf: -------------------------------------------------------------------------------- https://raw.githubusercontent.com/gillescastel/masterthesis/16b33d4121a8958e624bb0c9157151a63311b119/thesis/figures/self-indexing-morse-function-torus-tilted.pdf -------------------------------------------------------------------------------- /thesis/figures/self-indexing-morse-function-torus-tilted.pdf_tex: -------------------------------------------------------------------------------- 1 | %% Creator: Inkscape inkscape 0.92.4, www.inkscape.org 2 | %% PDF/EPS/PS + LaTeX output extension by Johan Engelen, 2010 3 | %% Accompanies image file 'self-indexing-morse-function-torus-tilted.pdf' (pdf, eps, ps) 4 | %% 5 | %% To include the image in your LaTeX document, write 6 | %% \input{.pdf_tex} 7 | %% instead of 8 | %% \includegraphics{.pdf} 9 | %% To scale the image, write 10 | %% \def\svgwidth{} 11 | %% \input{.pdf_tex} 12 | %% instead of 13 | %% \includegraphics[width=]{.pdf} 14 | %% 15 | %% Images with a different path to the parent latex file can 16 | %% be accessed with the `import' package (which may need to be 17 | %% installed) using 18 | %% \usepackage{import} 19 | %% in the preamble, and then including the image with 20 | %% \import{}{.pdf_tex} 21 | %% Alternatively, one can specify 22 | %% \graphicspath{{/}} 23 | %% 24 | %% For more information, please see info/svg-inkscape on CTAN: 25 | %% http://tug.ctan.org/tex-archive/info/svg-inkscape 26 | %% 27 | \begingroup% 28 | \makeatletter% 29 | \providecommand\color[2][]{% 30 | \errmessage{(Inkscape) Color is used for the text in Inkscape, but the package 'color.sty' is not loaded}% 31 | \renewcommand\color[2][]{}% 32 | }% 33 | \providecommand\transparent[1]{% 34 | \errmessage{(Inkscape) Transparency is used (non-zero) for the text in Inkscape, but the package 'transparent.sty' is not loaded}% 35 | \renewcommand\transparent[1]{}% 36 | }% 37 | \providecommand\rotatebox[2]{#2}% 38 | \newcommand*\fsize{\dimexpr\f@size pt\relax}% 39 | \newcommand*\lineheight[1]{\fontsize{\fsize}{#1\fsize}\selectfont}% 40 | \ifx\svgwidth\undefined% 41 | \setlength{\unitlength}{136.13206758bp}% 42 | \ifx\svgscale\undefined% 43 | \relax% 44 | \else% 45 | \setlength{\unitlength}{\unitlength * \real{\svgscale}}% 46 | \fi% 47 | \else% 48 | \setlength{\unitlength}{\svgwidth}% 49 | \fi% 50 | \global\let\svgwidth\undefined% 51 | \global\let\svgscale\undefined% 52 | \makeatother% 53 | \begin{picture}(1,0.68367693)% 54 | \lineheight{1}% 55 | \setlength\tabcolsep{0pt}% 56 | \put(0,0){\includegraphics[width=\unitlength,page=1]{self-indexing-morse-function-torus-tilted.pdf}}% 57 | \put(0.89201127,0.11282119){\color[rgb]{0,0,0}\makebox(0,0)[lt]{\lineheight{1.25}\smash{\begin{tabular}[t]{l}$0$\end{tabular}}}}% 58 | \put(0.89201127,0.32318714){\color[rgb]{0,0,0}\makebox(0,0)[lt]{\lineheight{1.25}\smash{\begin{tabular}[t]{l}$1$\end{tabular}}}}% 59 | \put(0.89201127,0.53402015){\color[rgb]{0,0,0}\makebox(0,0)[lt]{\lineheight{1.25}\smash{\begin{tabular}[t]{l}$2$\end{tabular}}}}% 60 | \put(0,0){\includegraphics[width=\unitlength,page=2]{self-indexing-morse-function-torus-tilted.pdf}}% 61 | \put(0.71590553,0.46717259){\color[rgb]{0,0,0}\makebox(0,0)[t]{\lineheight{1.25}\smash{\begin{tabular}[t]{c}$f$\end{tabular}}}}% 62 | \put(0,0){\includegraphics[width=\unitlength,page=3]{self-indexing-morse-function-torus-tilted.pdf}}% 63 | \end{picture}% 64 | \endgroup% 65 | -------------------------------------------------------------------------------- /thesis/figures/stabilization.pdf: -------------------------------------------------------------------------------- https://raw.githubusercontent.com/gillescastel/masterthesis/16b33d4121a8958e624bb0c9157151a63311b119/thesis/figures/stabilization.pdf -------------------------------------------------------------------------------- /thesis/figures/stabilization.pdf_tex: -------------------------------------------------------------------------------- 1 | %% Creator: Inkscape inkscape 0.92.4, www.inkscape.org 2 | %% PDF/EPS/PS + LaTeX output extension by Johan Engelen, 2010 3 | %% Accompanies image file 'stabilization.pdf' (pdf, eps, ps) 4 | %% 5 | %% To include the image in your LaTeX document, write 6 | %% \input{.pdf_tex} 7 | %% instead of 8 | %% \includegraphics{.pdf} 9 | %% To scale the image, write 10 | %% \def\svgwidth{} 11 | %% \input{.pdf_tex} 12 | %% instead of 13 | %% \includegraphics[width=]{.pdf} 14 | %% 15 | %% Images with a different path to the parent latex file can 16 | %% be accessed with the `import' package (which may need to be 17 | %% installed) using 18 | %% \usepackage{import} 19 | %% in the preamble, and then including the image with 20 | %% \import{}{.pdf_tex} 21 | %% Alternatively, one can specify 22 | %% \graphicspath{{/}} 23 | %% 24 | %% For more information, please see info/svg-inkscape on CTAN: 25 | %% http://tug.ctan.org/tex-archive/info/svg-inkscape 26 | %% 27 | \begingroup% 28 | \makeatletter% 29 | \providecommand\color[2][]{% 30 | \errmessage{(Inkscape) Color is used for the text in Inkscape, but the package 'color.sty' is not loaded}% 31 | \renewcommand\color[2][]{}% 32 | }% 33 | \providecommand\transparent[1]{% 34 | \errmessage{(Inkscape) Transparency is used (non-zero) for the text in Inkscape, but the package 'transparent.sty' is not loaded}% 35 | \renewcommand\transparent[1]{}% 36 | }% 37 | \providecommand\rotatebox[2]{#2}% 38 | \newcommand*\fsize{\dimexpr\f@size pt\relax}% 39 | \newcommand*\lineheight[1]{\fontsize{\fsize}{#1\fsize}\selectfont}% 40 | \ifx\svgwidth\undefined% 41 | \setlength{\unitlength}{127.06368634bp}% 42 | \ifx\svgscale\undefined% 43 | \relax% 44 | \else% 45 | \setlength{\unitlength}{\unitlength * \real{\svgscale}}% 46 | \fi% 47 | \else% 48 | \setlength{\unitlength}{\svgwidth}% 49 | \fi% 50 | \global\let\svgwidth\undefined% 51 | \global\let\svgscale\undefined% 52 | \makeatother% 53 | \begin{picture}(1,0.43359991)% 54 | \lineheight{1}% 55 | \setlength\tabcolsep{0pt}% 56 | \put(0,0){\includegraphics[width=\unitlength,page=1]{stabilization.pdf}}% 57 | \end{picture}% 58 | \endgroup% 59 | -------------------------------------------------------------------------------- /thesis/figures/stable-and-unstable-manifolds-are-manifiolds.pdf: -------------------------------------------------------------------------------- https://raw.githubusercontent.com/gillescastel/masterthesis/16b33d4121a8958e624bb0c9157151a63311b119/thesis/figures/stable-and-unstable-manifolds-are-manifiolds.pdf -------------------------------------------------------------------------------- /thesis/figures/stable-and-unstable-manifolds-are-manifiolds.pdf_tex: -------------------------------------------------------------------------------- 1 | %% Creator: Inkscape inkscape 0.92.4, www.inkscape.org 2 | %% PDF/EPS/PS + LaTeX output extension by Johan Engelen, 2010 3 | %% Accompanies image file 'stable-and-unstable-manifolds-are-manifiolds.pdf' (pdf, eps, ps) 4 | %% 5 | %% To include the image in your LaTeX document, write 6 | %% \input{.pdf_tex} 7 | %% instead of 8 | %% \includegraphics{.pdf} 9 | %% To scale the image, write 10 | %% \def\svgwidth{} 11 | %% \input{.pdf_tex} 12 | %% instead of 13 | %% \includegraphics[width=]{.pdf} 14 | %% 15 | %% Images with a different path to the parent latex file can 16 | %% be accessed with the `import' package (which may need to be 17 | %% installed) using 18 | %% \usepackage{import} 19 | %% in the preamble, and then including the image with 20 | %% \import{}{.pdf_tex} 21 | %% Alternatively, one can specify 22 | %% \graphicspath{{/}} 23 | %% 24 | %% For more information, please see info/svg-inkscape on CTAN: 25 | %% http://tug.ctan.org/tex-archive/info/svg-inkscape 26 | %% 27 | \begingroup% 28 | \makeatletter% 29 | \providecommand\color[2][]{% 30 | \errmessage{(Inkscape) Color is used for the text in Inkscape, but the package 'color.sty' is not loaded}% 31 | \renewcommand\color[2][]{}% 32 | }% 33 | \providecommand\transparent[1]{% 34 | \errmessage{(Inkscape) Transparency is used (non-zero) for the text in Inkscape, but the package 'transparent.sty' is not loaded}% 35 | \renewcommand\transparent[1]{}% 36 | }% 37 | \providecommand\rotatebox[2]{#2}% 38 | \newcommand*\fsize{\dimexpr\f@size pt\relax}% 39 | \newcommand*\lineheight[1]{\fontsize{\fsize}{#1\fsize}\selectfont}% 40 | \ifx\svgwidth\undefined% 41 | \setlength{\unitlength}{217.62021523bp}% 42 | \ifx\svgscale\undefined% 43 | \relax% 44 | \else% 45 | \setlength{\unitlength}{\unitlength * \real{\svgscale}}% 46 | \fi% 47 | \else% 48 | \setlength{\unitlength}{\svgwidth}% 49 | \fi% 50 | \global\let\svgwidth\undefined% 51 | \global\let\svgscale\undefined% 52 | \makeatother% 53 | \begin{picture}(1,0.89255803)% 54 | \lineheight{1}% 55 | \setlength\tabcolsep{0pt}% 56 | \put(0,0){\includegraphics[width=\unitlength,page=1]{stable-and-unstable-manifolds-are-manifiolds.pdf}}% 57 | \put(0.87058523,0.40745065){\color[rgb]{0,0,0}\makebox(0,0)[lt]{\lineheight{1.25}\smash{\begin{tabular}[t]{l}$x_1, \ldots, x_k$\end{tabular}}}}% 58 | \put(0.38921279,0.86614064){\color[rgb]{0,0,0}\makebox(0,0)[lt]{\lineheight{1.25}\smash{\begin{tabular}[t]{l}$x_{k+1}, \ldots, x_{n}$\end{tabular}}}}% 59 | \put(0.52023636,0.45321803){\color[rgb]{0,0,0}\makebox(0,0)[lt]{\lineheight{1.25}\smash{\begin{tabular}[t]{l}$\unstable{p}$\end{tabular}}}}% 60 | \put(0.43522169,0.75094219){\color[rgb]{0,0,0}\makebox(0,0)[lt]{\lineheight{1.25}\smash{\begin{tabular}[t]{l}$\stable{p}$\end{tabular}}}}% 61 | \put(0,0){\includegraphics[width=\unitlength,page=2]{stable-and-unstable-manifolds-are-manifiolds.pdf}}% 62 | \end{picture}% 63 | \endgroup% 64 | -------------------------------------------------------------------------------- /thesis/figures/stable-and-unstable-manifolds-are-manifiolds.svg.2020_12_13_11_17_24.0.pdf: -------------------------------------------------------------------------------- https://raw.githubusercontent.com/gillescastel/masterthesis/16b33d4121a8958e624bb0c9157151a63311b119/thesis/figures/stable-and-unstable-manifolds-are-manifiolds.svg.2020_12_13_11_17_24.0.pdf -------------------------------------------------------------------------------- /thesis/figures/stable-and-unstable-manifolds-are-manifiolds.svg.2020_12_13_11_17_24.0.pdf_tex: -------------------------------------------------------------------------------- 1 | %% Creator: Inkscape inkscape 0.92.4, www.inkscape.org 2 | %% PDF/EPS/PS + LaTeX output extension by Johan Engelen, 2010 3 | %% Accompanies image file 'stable-and-unstable-manifolds-are-manifiolds.svg.2020_12_13_11_17_24.0.pdf' (pdf, eps, ps) 4 | %% 5 | %% To include the image in your LaTeX document, write 6 | %% \input{.pdf_tex} 7 | %% instead of 8 | %% \includegraphics{.pdf} 9 | %% To scale the image, write 10 | %% \def\svgwidth{} 11 | %% \input{.pdf_tex} 12 | %% instead of 13 | %% \includegraphics[width=]{.pdf} 14 | %% 15 | %% Images with a different path to the parent latex file can 16 | %% be accessed with the `import' package (which may need to be 17 | %% installed) using 18 | %% \usepackage{import} 19 | %% in the preamble, and then including the image with 20 | %% \import{}{.pdf_tex} 21 | %% Alternatively, one can specify 22 | %% \graphicspath{{/}} 23 | %% 24 | %% For more information, please see info/svg-inkscape on CTAN: 25 | %% http://tug.ctan.org/tex-archive/info/svg-inkscape 26 | %% 27 | \begingroup% 28 | \makeatletter% 29 | \providecommand\color[2][]{% 30 | \errmessage{(Inkscape) Color is used for the text in Inkscape, but the package 'color.sty' is not loaded}% 31 | \renewcommand\color[2][]{}% 32 | }% 33 | \providecommand\transparent[1]{% 34 | \errmessage{(Inkscape) Transparency is used (non-zero) for the text in Inkscape, but the package 'transparent.sty' is not loaded}% 35 | \renewcommand\transparent[1]{}% 36 | }% 37 | \providecommand\rotatebox[2]{#2}% 38 | \newcommand*\fsize{\dimexpr\f@size pt\relax}% 39 | \newcommand*\lineheight[1]{\fontsize{\fsize}{#1\fsize}\selectfont}% 40 | \ifx\svgwidth\undefined% 41 | \setlength{\unitlength}{217.62021523bp}% 42 | \ifx\svgscale\undefined% 43 | \relax% 44 | \else% 45 | \setlength{\unitlength}{\unitlength * \real{\svgscale}}% 46 | \fi% 47 | \else% 48 | \setlength{\unitlength}{\svgwidth}% 49 | \fi% 50 | \global\let\svgwidth\undefined% 51 | \global\let\svgscale\undefined% 52 | \makeatother% 53 | \begin{picture}(1,0.89255803)% 54 | \lineheight{1}% 55 | \setlength\tabcolsep{0pt}% 56 | \put(0,0){\includegraphics[width=\unitlength,page=1]{stable-and-unstable-manifolds-are-manifiolds.svg.2020_12_13_11_17_24.0.pdf}}% 57 | \put(0.87058523,0.40745065){\color[rgb]{0,0,0}\makebox(0,0)[lt]{\lineheight{1.25}\smash{\begin{tabular}[t]{l}$x_1, \ldots, x_k$\end{tabular}}}}% 58 | \put(0.38921279,0.86614064){\color[rgb]{0,0,0}\makebox(0,0)[lt]{\lineheight{1.25}\smash{\begin{tabular}[t]{l}$x_{k+1}, \ldots, x_{n}$\end{tabular}}}}% 59 | \put(0.52023636,0.45321803){\color[rgb]{0,0,0}\makebox(0,0)[lt]{\lineheight{1.25}\smash{\begin{tabular}[t]{l}$\unstable{p}$\end{tabular}}}}% 60 | \put(0.43522169,0.60970795){\color[rgb]{0,0,0}\makebox(0,0)[lt]{\lineheight{1.25}\smash{\begin{tabular}[t]{l}$\stable{p}$\end{tabular}}}}% 61 | \put(0,0){\includegraphics[width=\unitlength,page=2]{stable-and-unstable-manifolds-are-manifiolds.svg.2020_12_13_11_17_24.0.pdf}}% 62 | \end{picture}% 63 | \endgroup% 64 | -------------------------------------------------------------------------------- /thesis/figures/stable-and-unstable-manifolds-are-manifiolds.svg.2020_12_13_11_21_18.0.pdf: -------------------------------------------------------------------------------- https://raw.githubusercontent.com/gillescastel/masterthesis/16b33d4121a8958e624bb0c9157151a63311b119/thesis/figures/stable-and-unstable-manifolds-are-manifiolds.svg.2020_12_13_11_21_18.0.pdf -------------------------------------------------------------------------------- /thesis/figures/stable-and-unstable-manifolds-are-manifiolds.svg.2020_12_13_11_21_18.0.pdf_tex: -------------------------------------------------------------------------------- 1 | %% Creator: Inkscape inkscape 0.92.4, www.inkscape.org 2 | %% PDF/EPS/PS + LaTeX output extension by Johan Engelen, 2010 3 | %% Accompanies image file 'stable-and-unstable-manifolds-are-manifiolds.svg.2020_12_13_11_21_18.0.pdf' (pdf, eps, ps) 4 | %% 5 | %% To include the image in your LaTeX document, write 6 | %% \input{.pdf_tex} 7 | %% instead of 8 | %% \includegraphics{.pdf} 9 | %% To scale the image, write 10 | %% \def\svgwidth{} 11 | %% \input{.pdf_tex} 12 | %% instead of 13 | %% \includegraphics[width=]{.pdf} 14 | %% 15 | %% Images with a different path to the parent latex file can 16 | %% be accessed with the `import' package (which may need to be 17 | %% installed) using 18 | %% \usepackage{import} 19 | %% in the preamble, and then including the image with 20 | %% \import{}{.pdf_tex} 21 | %% Alternatively, one can specify 22 | %% \graphicspath{{/}} 23 | %% 24 | %% For more information, please see info/svg-inkscape on CTAN: 25 | %% http://tug.ctan.org/tex-archive/info/svg-inkscape 26 | %% 27 | \begingroup% 28 | \makeatletter% 29 | \providecommand\color[2][]{% 30 | \errmessage{(Inkscape) Color is used for the text in Inkscape, but the package 'color.sty' is not loaded}% 31 | \renewcommand\color[2][]{}% 32 | }% 33 | \providecommand\transparent[1]{% 34 | \errmessage{(Inkscape) Transparency is used (non-zero) for the text in Inkscape, but the package 'transparent.sty' is not loaded}% 35 | \renewcommand\transparent[1]{}% 36 | }% 37 | \providecommand\rotatebox[2]{#2}% 38 | \newcommand*\fsize{\dimexpr\f@size pt\relax}% 39 | \newcommand*\lineheight[1]{\fontsize{\fsize}{#1\fsize}\selectfont}% 40 | \ifx\svgwidth\undefined% 41 | \setlength{\unitlength}{217.62021523bp}% 42 | \ifx\svgscale\undefined% 43 | \relax% 44 | \else% 45 | \setlength{\unitlength}{\unitlength * \real{\svgscale}}% 46 | \fi% 47 | \else% 48 | \setlength{\unitlength}{\svgwidth}% 49 | \fi% 50 | \global\let\svgwidth\undefined% 51 | \global\let\svgscale\undefined% 52 | \makeatother% 53 | \begin{picture}(1,0.89255803)% 54 | \lineheight{1}% 55 | \setlength\tabcolsep{0pt}% 56 | \put(0,0){\includegraphics[width=\unitlength,page=1]{stable-and-unstable-manifolds-are-manifiolds.svg.2020_12_13_11_21_18.0.pdf}}% 57 | \put(0.87058523,0.40745065){\color[rgb]{0,0,0}\makebox(0,0)[lt]{\lineheight{1.25}\smash{\begin{tabular}[t]{l}$x_1, \ldots, x_k$\end{tabular}}}}% 58 | \put(0.38921279,0.86614064){\color[rgb]{0,0,0}\makebox(0,0)[lt]{\lineheight{1.25}\smash{\begin{tabular}[t]{l}$x_{k+1}, \ldots, x_{n}$\end{tabular}}}}% 59 | \put(0.52023636,0.45321803){\color[rgb]{0,0,0}\makebox(0,0)[lt]{\lineheight{1.25}\smash{\begin{tabular}[t]{l}$\unstable{p}$\end{tabular}}}}% 60 | \put(0.43522169,0.60970795){\color[rgb]{0,0,0}\makebox(0,0)[lt]{\lineheight{1.25}\smash{\begin{tabular}[t]{l}$\stable{p}$\end{tabular}}}}% 61 | \put(0,0){\includegraphics[width=\unitlength,page=2]{stable-and-unstable-manifolds-are-manifiolds.svg.2020_12_13_11_21_18.0.pdf}}% 62 | \end{picture}% 63 | \endgroup% 64 | -------------------------------------------------------------------------------- /thesis/figures/test-figure.pdf: -------------------------------------------------------------------------------- https://raw.githubusercontent.com/gillescastel/masterthesis/16b33d4121a8958e624bb0c9157151a63311b119/thesis/figures/test-figure.pdf -------------------------------------------------------------------------------- /thesis/figures/test-figure.pdf_tex: -------------------------------------------------------------------------------- 1 | %% Creator: Inkscape inkscape 0.92.4, www.inkscape.org 2 | %% PDF/EPS/PS + LaTeX output extension by Johan Engelen, 2010 3 | %% Accompanies image file 'test-figure.pdf' (pdf, eps, ps) 4 | %% 5 | %% To include the image in your LaTeX document, write 6 | %% \input{.pdf_tex} 7 | %% instead of 8 | %% \includegraphics{.pdf} 9 | %% To scale the image, write 10 | %% \def\svgwidth{} 11 | %% \input{.pdf_tex} 12 | %% instead of 13 | %% \includegraphics[width=]{.pdf} 14 | %% 15 | %% Images with a different path to the parent latex file can 16 | %% be accessed with the `import' package (which may need to be 17 | %% installed) using 18 | %% \usepackage{import} 19 | %% in the preamble, and then including the image with 20 | %% \import{}{.pdf_tex} 21 | %% Alternatively, one can specify 22 | %% \graphicspath{{/}} 23 | %% 24 | %% For more information, please see info/svg-inkscape on CTAN: 25 | %% http://tug.ctan.org/tex-archive/info/svg-inkscape 26 | %% 27 | \begingroup% 28 | \makeatletter% 29 | \providecommand\color[2][]{% 30 | \errmessage{(Inkscape) Color is used for the text in Inkscape, but the package 'color.sty' is not loaded}% 31 | \renewcommand\color[2][]{}% 32 | }% 33 | \providecommand\transparent[1]{% 34 | \errmessage{(Inkscape) Transparency is used (non-zero) for the text in Inkscape, but the package 'transparent.sty' is not loaded}% 35 | \renewcommand\transparent[1]{}% 36 | }% 37 | \providecommand\rotatebox[2]{#2}% 38 | \newcommand*\fsize{\dimexpr\f@size pt\relax}% 39 | \newcommand*\lineheight[1]{\fontsize{\fsize}{#1\fsize}\selectfont}% 40 | \ifx\svgwidth\undefined% 41 | \setlength{\unitlength}{355.32585805bp}% 42 | \ifx\svgscale\undefined% 43 | \relax% 44 | \else% 45 | \setlength{\unitlength}{\unitlength * \real{\svgscale}}% 46 | \fi% 47 | \else% 48 | \setlength{\unitlength}{\svgwidth}% 49 | \fi% 50 | \global\let\svgwidth\undefined% 51 | \global\let\svgscale\undefined% 52 | \makeatother% 53 | \begin{picture}(1,0.72382302)% 54 | \lineheight{1}% 55 | \setlength\tabcolsep{0pt}% 56 | \put(0,0){\includegraphics[width=\unitlength,page=1]{test-figure.pdf}}% 57 | \end{picture}% 58 | \endgroup% 59 | -------------------------------------------------------------------------------- /thesis/figures/three-torus-handle-decomposition.pdf: -------------------------------------------------------------------------------- https://raw.githubusercontent.com/gillescastel/masterthesis/16b33d4121a8958e624bb0c9157151a63311b119/thesis/figures/three-torus-handle-decomposition.pdf -------------------------------------------------------------------------------- /thesis/figures/three-torus-handle-decomposition.pdf_tex: -------------------------------------------------------------------------------- 1 | %% Creator: Inkscape inkscape 0.92.4, www.inkscape.org 2 | %% PDF/EPS/PS + LaTeX output extension by Johan Engelen, 2010 3 | %% Accompanies image file 'three-torus-handle-decomposition.pdf' (pdf, eps, ps) 4 | %% 5 | %% To include the image in your LaTeX document, write 6 | %% \input{.pdf_tex} 7 | %% instead of 8 | %% \includegraphics{.pdf} 9 | %% To scale the image, write 10 | %% \def\svgwidth{} 11 | %% \input{.pdf_tex} 12 | %% instead of 13 | %% \includegraphics[width=]{.pdf} 14 | %% 15 | %% Images with a different path to the parent latex file can 16 | %% be accessed with the `import' package (which may need to be 17 | %% installed) using 18 | %% \usepackage{import} 19 | %% in the preamble, and then including the image with 20 | %% \import{}{.pdf_tex} 21 | %% Alternatively, one can specify 22 | %% \graphicspath{{/}} 23 | %% 24 | %% For more information, please see info/svg-inkscape on CTAN: 25 | %% http://tug.ctan.org/tex-archive/info/svg-inkscape 26 | %% 27 | \begingroup% 28 | \makeatletter% 29 | \providecommand\color[2][]{% 30 | \errmessage{(Inkscape) Color is used for the text in Inkscape, but the package 'color.sty' is not loaded}% 31 | \renewcommand\color[2][]{}% 32 | }% 33 | \providecommand\transparent[1]{% 34 | \errmessage{(Inkscape) Transparency is used (non-zero) for the text in Inkscape, but the package 'transparent.sty' is not loaded}% 35 | \renewcommand\transparent[1]{}% 36 | }% 37 | \providecommand\rotatebox[2]{#2}% 38 | \newcommand*\fsize{\dimexpr\f@size pt\relax}% 39 | \newcommand*\lineheight[1]{\fontsize{\fsize}{#1\fsize}\selectfont}% 40 | \ifx\svgwidth\undefined% 41 | \setlength{\unitlength}{984.17119064bp}% 42 | \ifx\svgscale\undefined% 43 | \relax% 44 | \else% 45 | \setlength{\unitlength}{\unitlength * \real{\svgscale}}% 46 | \fi% 47 | \else% 48 | \setlength{\unitlength}{\svgwidth}% 49 | \fi% 50 | \global\let\svgwidth\undefined% 51 | \global\let\svgscale\undefined% 52 | \makeatother% 53 | \begin{picture}(1,0.1296474)% 54 | \lineheight{1}% 55 | \setlength\tabcolsep{0pt}% 56 | \put(0,0){\includegraphics[width=\unitlength,page=1]{three-torus-handle-decomposition.pdf}}% 57 | \end{picture}% 58 | \endgroup% 59 | -------------------------------------------------------------------------------- /thesis/figures/three-torus-heegaard-splitting.pdf: -------------------------------------------------------------------------------- https://raw.githubusercontent.com/gillescastel/masterthesis/16b33d4121a8958e624bb0c9157151a63311b119/thesis/figures/three-torus-heegaard-splitting.pdf -------------------------------------------------------------------------------- /thesis/figures/three-torus-heegaard-splitting.pdf_tex: -------------------------------------------------------------------------------- 1 | %% Creator: Inkscape inkscape 0.92.4, www.inkscape.org 2 | %% PDF/EPS/PS + LaTeX output extension by Johan Engelen, 2010 3 | %% Accompanies image file 'three-torus-heegaard-splitting.pdf' (pdf, eps, ps) 4 | %% 5 | %% To include the image in your LaTeX document, write 6 | %% \input{.pdf_tex} 7 | %% instead of 8 | %% \includegraphics{.pdf} 9 | %% To scale the image, write 10 | %% \def\svgwidth{} 11 | %% \input{.pdf_tex} 12 | %% instead of 13 | %% \includegraphics[width=]{.pdf} 14 | %% 15 | %% Images with a different path to the parent latex file can 16 | %% be accessed with the `import' package (which may need to be 17 | %% installed) using 18 | %% \usepackage{import} 19 | %% in the preamble, and then including the image with 20 | %% \import{}{.pdf_tex} 21 | %% Alternatively, one can specify 22 | %% \graphicspath{{/}} 23 | %% 24 | %% For more information, please see info/svg-inkscape on CTAN: 25 | %% http://tug.ctan.org/tex-archive/info/svg-inkscape 26 | %% 27 | \begingroup% 28 | \makeatletter% 29 | \providecommand\color[2][]{% 30 | \errmessage{(Inkscape) Color is used for the text in Inkscape, but the package 'color.sty' is not loaded}% 31 | \renewcommand\color[2][]{}% 32 | }% 33 | \providecommand\transparent[1]{% 34 | \errmessage{(Inkscape) Transparency is used (non-zero) for the text in Inkscape, but the package 'transparent.sty' is not loaded}% 35 | \renewcommand\transparent[1]{}% 36 | }% 37 | \providecommand\rotatebox[2]{#2}% 38 | \newcommand*\fsize{\dimexpr\f@size pt\relax}% 39 | \newcommand*\lineheight[1]{\fontsize{\fsize}{#1\fsize}\selectfont}% 40 | \ifx\svgwidth\undefined% 41 | \setlength{\unitlength}{272.1262654bp}% 42 | \ifx\svgscale\undefined% 43 | \relax% 44 | \else% 45 | \setlength{\unitlength}{\unitlength * \real{\svgscale}}% 46 | \fi% 47 | \else% 48 | \setlength{\unitlength}{\svgwidth}% 49 | \fi% 50 | \global\let\svgwidth\undefined% 51 | \global\let\svgscale\undefined% 52 | \makeatother% 53 | \begin{picture}(1,0.64330452)% 54 | \lineheight{1}% 55 | \setlength\tabcolsep{0pt}% 56 | \put(0,0){\includegraphics[width=\unitlength,page=1]{three-torus-heegaard-splitting.pdf}}% 57 | \put(0.74858404,0.53727573){\color[rgb]{0,0,0}\makebox(0,0)[lt]{\lineheight{1.25}\smash{\begin{tabular}[t]{l}$TODO$\end{tabular}}}}% 58 | \end{picture}% 59 | \endgroup% 60 | -------------------------------------------------------------------------------- /thesis/figures/tilted-klein-bottle-over-z.pdf: -------------------------------------------------------------------------------- https://raw.githubusercontent.com/gillescastel/masterthesis/16b33d4121a8958e624bb0c9157151a63311b119/thesis/figures/tilted-klein-bottle-over-z.pdf -------------------------------------------------------------------------------- /thesis/figures/tilted-torus.pdf: -------------------------------------------------------------------------------- https://raw.githubusercontent.com/gillescastel/masterthesis/16b33d4121a8958e624bb0c9157151a63311b119/thesis/figures/tilted-torus.pdf -------------------------------------------------------------------------------- /thesis/figures/torus-height-function-stable-and-unstable-manifolds.pdf: -------------------------------------------------------------------------------- https://raw.githubusercontent.com/gillescastel/masterthesis/16b33d4121a8958e624bb0c9157151a63311b119/thesis/figures/torus-height-function-stable-and-unstable-manifolds.pdf -------------------------------------------------------------------------------- /thesis/figures/torus-homology.pdf: -------------------------------------------------------------------------------- https://raw.githubusercontent.com/gillescastel/masterthesis/16b33d4121a8958e624bb0c9157151a63311b119/thesis/figures/torus-homology.pdf -------------------------------------------------------------------------------- /thesis/figures/torus-homology.pdf_tex: -------------------------------------------------------------------------------- 1 | %% Creator: Inkscape inkscape 0.92.4, www.inkscape.org 2 | %% PDF/EPS/PS + LaTeX output extension by Johan Engelen, 2010 3 | %% Accompanies image file 'torus-homology.pdf' (pdf, eps, ps) 4 | %% 5 | %% To include the image in your LaTeX document, write 6 | %% \input{.pdf_tex} 7 | %% instead of 8 | %% \includegraphics{.pdf} 9 | %% To scale the image, write 10 | %% \def\svgwidth{} 11 | %% \input{.pdf_tex} 12 | %% instead of 13 | %% \includegraphics[width=]{.pdf} 14 | %% 15 | %% Images with a different path to the parent latex file can 16 | %% be accessed with the `import' package (which may need to be 17 | %% installed) using 18 | %% \usepackage{import} 19 | %% in the preamble, and then including the image with 20 | %% \import{}{.pdf_tex} 21 | %% Alternatively, one can specify 22 | %% \graphicspath{{/}} 23 | %% 24 | %% For more information, please see info/svg-inkscape on CTAN: 25 | %% http://tug.ctan.org/tex-archive/info/svg-inkscape 26 | %% 27 | \begingroup% 28 | \makeatletter% 29 | \providecommand\color[2][]{% 30 | \errmessage{(Inkscape) Color is used for the text in Inkscape, but the package 'color.sty' is not loaded}% 31 | \renewcommand\color[2][]{}% 32 | }% 33 | \providecommand\transparent[1]{% 34 | \errmessage{(Inkscape) Transparency is used (non-zero) for the text in Inkscape, but the package 'transparent.sty' is not loaded}% 35 | \renewcommand\transparent[1]{}% 36 | }% 37 | \providecommand\rotatebox[2]{#2}% 38 | \newcommand*\fsize{\dimexpr\f@size pt\relax}% 39 | \newcommand*\lineheight[1]{\fontsize{\fsize}{#1\fsize}\selectfont}% 40 | \ifx\svgwidth\undefined% 41 | \setlength{\unitlength}{377.54079744bp}% 42 | \ifx\svgscale\undefined% 43 | \relax% 44 | \else% 45 | \setlength{\unitlength}{\unitlength * \real{\svgscale}}% 46 | \fi% 47 | \else% 48 | \setlength{\unitlength}{\svgwidth}% 49 | \fi% 50 | \global\let\svgwidth\undefined% 51 | \global\let\svgscale\undefined% 52 | \makeatother% 53 | \begin{picture}(1,0.34017768)% 54 | \lineheight{1}% 55 | \setlength\tabcolsep{0pt}% 56 | \put(0,0){\includegraphics[width=\unitlength,page=1]{torus-homology.pdf}}% 57 | \put(0.16648604,0.00355586){\color[rgb]{0,0,0}\makebox(0,0)[t]{\lineheight{1.25}\smash{\begin{tabular}[t]{c}$S^{1}$\end{tabular}}}}% 58 | \put(0.40946078,0.00355586){\color[rgb]{0,0,0}\makebox(0,0)[t]{\lineheight{1.25}\smash{\begin{tabular}[t]{c}$T^{2}$\end{tabular}}}}% 59 | \put(0.74614919,0.00355586){\color[rgb]{0,0,0}\makebox(0,0)[t]{\lineheight{1.25}\smash{\begin{tabular}[t]{c}$T^{3}$\end{tabular}}}}% 60 | \end{picture}% 61 | \endgroup% 62 | -------------------------------------------------------------------------------- /thesis/figures/torus-tilted-height-function-stable-and-unstable-manifolds.pdf: -------------------------------------------------------------------------------- https://raw.githubusercontent.com/gillescastel/masterthesis/16b33d4121a8958e624bb0c9157151a63311b119/thesis/figures/torus-tilted-height-function-stable-and-unstable-manifolds.pdf -------------------------------------------------------------------------------- /thesis/figures/transversality-examples.pdf: -------------------------------------------------------------------------------- https://raw.githubusercontent.com/gillescastel/masterthesis/16b33d4121a8958e624bb0c9157151a63311b119/thesis/figures/transversality-examples.pdf -------------------------------------------------------------------------------- /thesis/figures/transversality-examples.pdf_tex: -------------------------------------------------------------------------------- 1 | %% Creator: Inkscape inkscape 0.92.4, www.inkscape.org 2 | %% PDF/EPS/PS + LaTeX output extension by Johan Engelen, 2010 3 | %% Accompanies image file 'transversality-examples.pdf' (pdf, eps, ps) 4 | %% 5 | %% To include the image in your LaTeX document, write 6 | %% \input{.pdf_tex} 7 | %% instead of 8 | %% \includegraphics{.pdf} 9 | %% To scale the image, write 10 | %% \def\svgwidth{} 11 | %% \input{.pdf_tex} 12 | %% instead of 13 | %% \includegraphics[width=]{.pdf} 14 | %% 15 | %% Images with a different path to the parent latex file can 16 | %% be accessed with the `import' package (which may need to be 17 | %% installed) using 18 | %% \usepackage{import} 19 | %% in the preamble, and then including the image with 20 | %% \import{}{.pdf_tex} 21 | %% Alternatively, one can specify 22 | %% \graphicspath{{/}} 23 | %% 24 | %% For more information, please see info/svg-inkscape on CTAN: 25 | %% http://tug.ctan.org/tex-archive/info/svg-inkscape 26 | %% 27 | \begingroup% 28 | \makeatletter% 29 | \providecommand\color[2][]{% 30 | \errmessage{(Inkscape) Color is used for the text in Inkscape, but the package 'color.sty' is not loaded}% 31 | \renewcommand\color[2][]{}% 32 | }% 33 | \providecommand\transparent[1]{% 34 | \errmessage{(Inkscape) Transparency is used (non-zero) for the text in Inkscape, but the package 'transparent.sty' is not loaded}% 35 | \renewcommand\transparent[1]{}% 36 | }% 37 | \providecommand\rotatebox[2]{#2}% 38 | \newcommand*\fsize{\dimexpr\f@size pt\relax}% 39 | \newcommand*\lineheight[1]{\fontsize{\fsize}{#1\fsize}\selectfont}% 40 | \ifx\svgwidth\undefined% 41 | \setlength{\unitlength}{645.19365926bp}% 42 | \ifx\svgscale\undefined% 43 | \relax% 44 | \else% 45 | \setlength{\unitlength}{\unitlength * \real{\svgscale}}% 46 | \fi% 47 | \else% 48 | \setlength{\unitlength}{\svgwidth}% 49 | \fi% 50 | \global\let\svgwidth\undefined% 51 | \global\let\svgscale\undefined% 52 | \makeatother% 53 | \begin{picture}(1,0.14858025)% 54 | \lineheight{1}% 55 | \setlength\tabcolsep{0pt}% 56 | \put(0,0){\includegraphics[width=\unitlength,page=1]{transversality-examples.pdf}}% 57 | \put(0.09891516,-0.01799937){\color[rgb]{0,0,0}\makebox(0,0)[lt]{\lineheight{1.25}\smash{\begin{tabular}[t]{l}$\tcap$\end{tabular}}}}% 58 | \put(0.3680634,-0.01799937){\color[rgb]{0,0,0}\makebox(0,0)[lt]{\lineheight{1.25}\smash{\begin{tabular}[t]{l}$\tcap$\end{tabular}}}}% 59 | \put(0.62932645,-0.01799937){\color[rgb]{0,0,0}\makebox(0,0)[lt]{\lineheight{1.25}\smash{\begin{tabular}[t]{l}$\not\tcap$\end{tabular}}}}% 60 | \put(0.89398001,-0.01799937){\color[rgb]{0,0,0}\makebox(0,0)[lt]{\lineheight{1.25}\smash{\begin{tabular}[t]{l}$\not\tcap$\end{tabular}}}}% 61 | \end{picture}% 62 | \endgroup% 63 | -------------------------------------------------------------------------------- /thesis/figures/when-can-we-attach-multiple-handles-at-the-same-time.pdf: -------------------------------------------------------------------------------- https://raw.githubusercontent.com/gillescastel/masterthesis/16b33d4121a8958e624bb0c9157151a63311b119/thesis/figures/when-can-we-attach-multiple-handles-at-the-same-time.pdf -------------------------------------------------------------------------------- /thesis/figures/when-can-we-not-attach-multiple-handles-at-the-same-time.pdf: -------------------------------------------------------------------------------- https://raw.githubusercontent.com/gillescastel/masterthesis/16b33d4121a8958e624bb0c9157151a63311b119/thesis/figures/when-can-we-not-attach-multiple-handles-at-the-same-time.pdf -------------------------------------------------------------------------------- /thesis/figures/whitneys-theorem-model-isotopy.pdf: -------------------------------------------------------------------------------- https://raw.githubusercontent.com/gillescastel/masterthesis/16b33d4121a8958e624bb0c9157151a63311b119/thesis/figures/whitneys-theorem-model-isotopy.pdf -------------------------------------------------------------------------------- /thesis/figures/whitneys-theorem-proof-model.pdf: -------------------------------------------------------------------------------- https://raw.githubusercontent.com/gillescastel/masterthesis/16b33d4121a8958e624bb0c9157151a63311b119/thesis/figures/whitneys-theorem-proof-model.pdf -------------------------------------------------------------------------------- /thesis/figures/without-zero-handles.pdf: -------------------------------------------------------------------------------- https://raw.githubusercontent.com/gillescastel/masterthesis/16b33d4121a8958e624bb0c9157151a63311b119/thesis/figures/without-zero-handles.pdf -------------------------------------------------------------------------------- /thesis/figures/without-zero-handles.pdf_tex: -------------------------------------------------------------------------------- 1 | %% Creator: Inkscape inkscape 0.92.4, www.inkscape.org 2 | %% PDF/EPS/PS + LaTeX output extension by Johan Engelen, 2010 3 | %% Accompanies image file 'without-zero-handles.pdf' (pdf, eps, ps) 4 | %% 5 | %% To include the image in your LaTeX document, write 6 | %% \input{.pdf_tex} 7 | %% instead of 8 | %% \includegraphics{.pdf} 9 | %% To scale the image, write 10 | %% \def\svgwidth{} 11 | %% \input{.pdf_tex} 12 | %% instead of 13 | %% \includegraphics[width=]{.pdf} 14 | %% 15 | %% Images with a different path to the parent latex file can 16 | %% be accessed with the `import' package (which may need to be 17 | %% installed) using 18 | %% \usepackage{import} 19 | %% in the preamble, and then including the image with 20 | %% \import{}{.pdf_tex} 21 | %% Alternatively, one can specify 22 | %% \graphicspath{{/}} 23 | %% 24 | %% For more information, please see info/svg-inkscape on CTAN: 25 | %% http://tug.ctan.org/tex-archive/info/svg-inkscape 26 | %% 27 | \begingroup% 28 | \makeatletter% 29 | \providecommand\color[2][]{% 30 | \errmessage{(Inkscape) Color is used for the text in Inkscape, but the package 'color.sty' is not loaded}% 31 | \renewcommand\color[2][]{}% 32 | }% 33 | \providecommand\transparent[1]{% 34 | \errmessage{(Inkscape) Transparency is used (non-zero) for the text in Inkscape, but the package 'transparent.sty' is not loaded}% 35 | \renewcommand\transparent[1]{}% 36 | }% 37 | \providecommand\rotatebox[2]{#2}% 38 | \newcommand*\fsize{\dimexpr\f@size pt\relax}% 39 | \newcommand*\lineheight[1]{\fontsize{\fsize}{#1\fsize}\selectfont}% 40 | \ifx\svgwidth\undefined% 41 | \setlength{\unitlength}{181.46386334bp}% 42 | \ifx\svgscale\undefined% 43 | \relax% 44 | \else% 45 | \setlength{\unitlength}{\unitlength * \real{\svgscale}}% 46 | \fi% 47 | \else% 48 | \setlength{\unitlength}{\svgwidth}% 49 | \fi% 50 | \global\let\svgwidth\undefined% 51 | \global\let\svgscale\undefined% 52 | \makeatother% 53 | \begin{picture}(1,0.65907063)% 54 | \lineheight{1}% 55 | \setlength\tabcolsep{0pt}% 56 | \put(0,0){\includegraphics[width=\unitlength,page=1]{without-zero-handles.pdf}}% 57 | \end{picture}% 58 | \endgroup% 59 | -------------------------------------------------------------------------------- /thesis/kuleuven-template/LogoKULeuven.png: -------------------------------------------------------------------------------- https://raw.githubusercontent.com/gillescastel/masterthesis/16b33d4121a8958e624bb0c9157151a63311b119/thesis/kuleuven-template/LogoKULeuven.png -------------------------------------------------------------------------------- /thesis/kuleuven-template/covers.pdf: -------------------------------------------------------------------------------- https://raw.githubusercontent.com/gillescastel/masterthesis/16b33d4121a8958e624bb0c9157151a63311b119/thesis/kuleuven-template/covers.pdf -------------------------------------------------------------------------------- /thesis/kuleuven-template/sedes.png: -------------------------------------------------------------------------------- https://raw.githubusercontent.com/gillescastel/masterthesis/16b33d4121a8958e624bb0c9157151a63311b119/thesis/kuleuven-template/sedes.png -------------------------------------------------------------------------------- /thesis/master.tex: -------------------------------------------------------------------------------- 1 | 2 | \documentclass[working]{tuftebook} 3 | 4 | \input{preamble.tex} 5 | \input{symbols.tex} 6 | \usepackage{pdfpages} 7 | 8 | \usepackage{lipsum} 9 | \usepackage{parskip} 10 | \usepackage{titletoc} 11 | 12 | \newcommand\circled[1]{ 13 | \begin{tikzpicture}[baseline=(char.base)]% 14 | \node[circle,draw,inner sep=1pt] (char) {\textsf{#1}};% 15 | \end{tikzpicture}} 16 | % minicircle for in figures! 17 | \newcommand\mc[1]{\footnotesize\circled{#1}} 18 | 19 | \usepackage{cmbright} 20 | \usepackage{bm} 21 | 22 | % \usepackage{eso-pic} % put things into background 23 | % \usepackage{lipsum} % for sample text 24 | 25 | % \definecolor{reallylightgray}{HTML}{FAFAFA} 26 | % \AddToShipoutPicture{% from package eso-pic: put something to the background 27 | % \ifthenelse{\isodd{\thepage}}{ 28 | % % ODD page: left bar 29 | % \AtPageLowerLeft{% start the bar at the left bottom of the page 30 | % \put(\LenToUnit{\dimexpr\paperwidth-222pt},0){% move it to the top right 31 | % \color{reallylightgray}\rule{222pt}{297mm}% 32 | % }% 33 | % }% 34 | % }% 35 | % {% 36 | % \AtPageLowerLeft{% put it at the left bottom of the page 37 | % \color{reallylightgray}\rule{222pt}{297mm}% 38 | % }% 39 | % }% 40 | % } 41 | 42 | \title{Morse theory} 43 | \date{Academic year 2020--2021} 44 | \begin{document} 45 | 46 | \renewcommand{\thepage}{\roman{page}} 47 | \includepdf[pages=1, fitpaper=true]{./kuleuven-template/covers.pdf} 48 | \thispagestyle{empty} 49 | \input{copyright.tex} 50 | \pagestyle{plain} 51 | \setcounter{page}{0} 52 | \input{preface.tex} 53 | \input{summary.tex} 54 | \listofsymbols 55 | \tableofcontents 56 | \cleardoublepage 57 | \renewcommand{\thepage}{\arabic{page}} 58 | \setcounter{page}{1} 59 | \pagestyle{normal} 60 | \input{chap0.tex} 61 | \input{chap1.tex} 62 | \input{chap2.tex} 63 | \input{chap3.tex} 64 | \input{chap4.tex} 65 | \input{chap5.tex} 66 | % \input{todo.tex} 67 | \input{conclusion.tex} 68 | % \input{chap-outlook.tex} 69 | 70 | 71 | \printbibliography 72 | \includepdf[pages=2, fitpaper=true]{./kuleuven-template/covers.pdf} 73 | \end{document} 74 | -------------------------------------------------------------------------------- /thesis/notebooks/three-torus/output.png: -------------------------------------------------------------------------------- https://raw.githubusercontent.com/gillescastel/masterthesis/16b33d4121a8958e624bb0c9157151a63311b119/thesis/notebooks/three-torus/output.png -------------------------------------------------------------------------------- /thesis/preface.tex: -------------------------------------------------------------------------------- 1 | \chapter*{Preface} 2 | \label{ch:preface} 3 | \addcontentsline{toc}{chapter}{\nameref{ch:preface}} 4 | 5 | This thesis is on Morse theory, 6 | the study of nice real valued functions on manifolds, 7 | called Morse functions. 8 | While elementary, they provide great insight in the structure of manifolds, eventually leading to some of the most important theorems in differential topology. 9 | The goal of this thesis is to prove one of them, namely the generalized Poincaré conjecture in higher dimensions, stating that a homotopy sphere is a topological sphere. 10 | 11 | This thesis could not have been written without the help of many people. 12 | 13 | First and foremost, I would like to thank Dr.~Charlotte Kirchhoff-Lukat for proposing this subject and supervising me throughout my journey. 14 | Charlotte, thank you for exposing me to the world of Morse theory and its many related topics. 15 | Thank you for your advice, patience, and the weekly chats which kept me motivated through the year. 16 | 17 | I would like to thank Prof.~Joeri Van der Veken and Dr.~François Thilmany for reading and evaluating this thesis. 18 | 19 | I would like to thank my family for their support, giving me the opportunity to make this possible. 20 | 21 | Lastly, Marie, thank you for the whiteboard in front of which we have spent many hours together. 22 | It was essential for finishing this thesis. 23 | Thank you for listening to my never ending rambles on Morse theory, proofreading my thesis, being the test subject for my presentations and for the much needed distraction. 24 | 25 | \hfill \emph{Gilles, June 2021} 26 | -------------------------------------------------------------------------------- /thesis/scratchpads/2020-11-13-Note-16-55.xoj: -------------------------------------------------------------------------------- https://raw.githubusercontent.com/gillescastel/masterthesis/16b33d4121a8958e624bb0c9157151a63311b119/thesis/scratchpads/2020-11-13-Note-16-55.xoj -------------------------------------------------------------------------------- /thesis/todo.tex: -------------------------------------------------------------------------------- 1 | \chapter*{TODO} 2 | --------------------------------------------------------------------------------