├── .gitignore ├── README.md ├── algebraic-topology ├── figures │ ├── antipode-preserving-maps.pdf │ ├── antipode-preserving-maps.pdf_tex │ ├── antipode-preserving-maps.svg │ ├── base-case-of-theorem.pdf │ ├── base-case-of-theorem.pdf_tex │ ├── base-case-of-theorem.svg │ ├── boundary-operator.pdf │ ├── boundary-operator.pdf_tex │ ├── boundary-operator.svg │ ├── chain-homotopic-proof.pdf │ ├── chain-homotopic-proof.pdf_tex │ ├── chain-homotopic-proof.svg │ ├── covering-space-example-2.pdf │ ├── covering-space-example-2.pdf_tex │ ├── covering-space-example-2.svg │ ├── covering-space-example.pdf │ ├── covering-space-example.pdf_tex │ ├── covering-space-example.svg │ ├── definition-of-suspension-general.pdf │ ├── definition-of-suspension-general.pdf_tex │ ├── definition-of-suspension-general.svg │ ├── definition-of-suspension.pdf │ ├── definition-of-suspension.pdf_tex │ ├── definition-of-suspension.svg │ ├── definition-singular-p-simplex.pdf │ ├── definition-singular-p-simplex.pdf_tex │ ├── definition-singular-p-simplex.svg │ ├── deformation-rectract-example-2.pdf │ ├── deformation-rectract-example-2.pdf_tex │ ├── deformation-rectract-example-2.svg │ ├── deformation-retract-example.pdf │ ├── deformation-retract-example.pdf_tex │ ├── deformation-retract-example.svg │ ├── dependence-of-base-point.pdf │ ├── dependence-of-base-point.pdf_tex │ ├── dependence-of-base-point.svg │ ├── evenly-covered.pdf │ ├── evenly-covered.pdf_tex │ ├── evenly-covered.svg │ ├── example-covering-fundamental-group.pdf │ ├── example-covering-fundamental-group.pdf_tex │ ├── example-covering-fundamental-group.svg │ ├── example-with-four-elements.pdf │ ├── example-with-four-elements.pdf_tex │ ├── example-with-four-elements.svg │ ├── figure-8-not-abelian.pdf │ ├── figure-8-not-abelian.pdf_tex │ ├── figure-8-not-abelian.png │ ├── figure-8-not-abelian.svg │ ├── figure-8-space.pdf │ ├── figure-8-space.pdf_tex │ ├── figure-8-space.svg │ ├── figure-eight-free-product-group.pdf │ ├── figure-eight-free-product-group.pdf_tex │ ├── figure-eight-free-product-group.svg │ ├── figure-eight-theta-space.pdf │ ├── figure-eight-theta-space.pdf_tex │ ├── figure-eight-theta-space.svg │ ├── fundamental-group-of-a-poolring-for-twins.pdf │ ├── fundamental-group-of-a-poolring-for-twins.pdf_tex │ ├── fundamental-group-of-a-poolring-for-twins.svg │ ├── fundamental-group-of-circle-lemma.pdf │ ├── fundamental-group-of-circle-lemma.pdf_tex │ ├── fundamental-group-of-circle-lemma.svg │ ├── fundamental-group-of-the-torus-using-van-kampen-2.pdf │ ├── fundamental-group-of-the-torus-using-van-kampen-2.pdf_tex │ ├── fundamental-group-of-the-torus-using-van-kampen-2.svg │ ├── fundamental-group-of-the-torus-using-van-kampen.pdf │ ├── fundamental-group-of-the-torus-using-van-kampen.pdf_tex │ ├── fundamental-group-of-the-torus-using-van-kampen.svg │ ├── general-lifting-lemma-continuous.pdf │ ├── general-lifting-lemma-continuous.pdf_tex │ ├── general-lifting-lemma-continuous.svg │ ├── general-lifting-lemma.pdf │ ├── general-lifting-lemma.pdf_tex │ ├── general-lifting-lemma.svg │ ├── hairy-ball-theorem.pdf │ ├── hairy-ball-theorem.pdf_tex │ ├── hairy-ball-theorem.svg │ ├── ham-sandwich-theorem.pdf │ ├── ham-sandwich-theorem.pdf_tex │ ├── ham-sandwich-theorem.svg │ ├── homology-connection-with-continuous-map.pdf │ ├── homology-connection-with-continuous-map.pdf_tex │ ├── homology-connection-with-continuous-map.svg │ ├── homology-of-circle.pdf │ ├── homology-of-circle.pdf_tex │ ├── homology-of-circle.svg │ ├── homology-of-convex-subset-of-rn.pdf │ ├── homology-of-convex-subset-of-rn.pdf_tex │ ├── homology-of-convex-subset-of-rn.svg │ ├── homology-of-torus.pdf │ ├── homology-of-torus.pdf_tex │ ├── homology-of-torus.svg │ ├── homology-of-torus.svg.2019_12_10_13_10_01.0.pdf │ ├── homology-of-torus.svg.2019_12_10_13_10_01.0.pdf_tex │ ├── homology-of-torus.svg.2019_12_10_13_10_01.0.svg │ ├── homotopy-general-example.pdf │ ├── homotopy-general-example.pdf_tex │ ├── homotopy-general-example.svg │ ├── infinite-earring.pdf │ ├── infinite-earring.pdf_tex │ ├── infinite-earring.svg │ ├── intuition-homology.pdf │ ├── intuition-homology.pdf_tex │ ├── intuition-homology.svg │ ├── isomorphism-of-groups.pdf │ ├── isomorphism-of-groups.pdf_tex │ ├── isomorphism-of-groups.svg │ ├── klein-bottle-homology.pdf │ ├── klein-bottle-homology.pdf_tex │ ├── klein-bottle-homology.svg │ ├── lemma-universal-covering-space.pdf │ ├── lemma-universal-covering-space.pdf_tex │ ├── lemma-universal-covering-space.svg │ ├── lift-of-a-path-homotopy.pdf │ ├── lift-of-a-path-homotopy.pdf_tex │ ├── lift-of-a-path-homotopy.svg │ ├── lift-of-path-homotopy-2.pdf │ ├── lift-of-path-homotopy-2.pdf_tex │ ├── lift-of-path-homotopy-2.svg │ ├── lifting-correspondence.pdf │ ├── lifting-correspondence.pdf_tex │ ├── lifting-correspondence.svg │ ├── no-antipodal-preserving-map-from-s2-to-s1.pdf │ ├── no-antipodal-preserving-map-from-s2-to-s1.pdf_tex │ ├── no-antipodal-preserving-map-from-s2-to-s1.svg │ ├── projective-plane-example.pdf │ ├── projective-plane-example.pdf_tex │ ├── projective-plane-example.svg │ ├── proof-fixed-point-brouwer.pdf │ ├── proof-fixed-point-brouwer.pdf_tex │ ├── proof-fixed-point-brouwer.svg │ ├── proof-lemma-7.pdf │ ├── proof-lemma-7.pdf_tex │ ├── proof-lemma-7.svg │ ├── proof-path-gamma.png │ ├── proof-path.pdf │ ├── proof-path.pdf_tex │ ├── proof-path.svg │ ├── proof-prop-123.pdf │ ├── proof-prop-123.pdf_tex │ ├── proof-prop-123.svg │ ├── testfiguur.pdf │ ├── testfiguur.pdf_tex │ ├── testfiguur.svg │ ├── theorem-59-1.pdf │ ├── theorem-59-1.pdf_tex │ ├── theorem-59-1.svg │ ├── torus-covering.pdf │ ├── torus-covering.pdf_tex │ ├── torus-covering.svg │ ├── tweeling-zwemband.pdf │ ├── tweeling-zwemband.pdf_tex │ ├── tweeling-zwemband.svg │ ├── wedge-circles.pdf │ ├── wedge-circles.pdf_tex │ ├── wedge-circles.svg │ ├── well-defined-general-lifting-lemma.pdf │ ├── well-defined-general-lifting-lemma.pdf_tex │ └── well-defined-general-lifting-lemma.svg ├── les_01.tex ├── les_02.tex ├── les_03.tex ├── les_04.tex ├── les_05.tex ├── les_06.tex ├── les_07.tex ├── les_08.tex ├── les_09.tex ├── les_10.tex ├── master.tex └── preamble.tex ├── differential-geometry ├── figures │ ├── GregoryvanKruijsdijk.pdf │ ├── canonical-form-of-commuting-vector-fields.pdf │ ├── canonical-form-of-commuting-vector-fields.pdf_tex │ ├── canonical-form-of-commuting-vector-fields.svg │ ├── circle-submanifold-example.pdf │ ├── circle-submanifold-example.pdf_tex │ ├── circle-submanifold-example.svg │ ├── compatible.pdf │ ├── compatible.pdf_tex │ ├── compatible.svg │ ├── definition-of-a-section.pdf │ ├── definition-of-a-section.pdf_tex │ ├── definition-of-a-section.svg │ ├── definition-of-foliation.pdf │ ├── definition-of-foliation.pdf_tex │ ├── definition-of-foliation.svg │ ├── example-of-a-vector-bundle-that-doesnt-admit-a-frame.pdf │ ├── example-of-a-vector-bundle-that-doesnt-admit-a-frame.pdf_tex │ ├── example-of-a-vector-bundle-that-doesnt-admit-a-frame.svg │ ├── example-of-fiber-bundle.pdf │ ├── example-of-fiber-bundle.pdf_tex │ ├── example-of-fiber-bundle.svg │ ├── example-submersion.pdf │ ├── example-submersion.pdf_tex │ ├── example-submersion.svg │ ├── f-related.pdf │ ├── f-related.pdf_tex │ ├── f-related.svg │ ├── figure-1.pdf │ ├── figure-1.pdf_tex │ ├── figure-1.svg │ ├── homotopy-definition.pdf │ ├── homotopy-definition.pdf_tex │ ├── homotopy-definition.svg │ ├── interpretation-of-lie-bracket-lemma-flow.pdf │ ├── interpretation-of-lie-bracket-lemma-flow.pdf_tex │ ├── interpretation-of-lie-bracket-lemma-flow.svg │ ├── mobius-strip.pdf │ ├── mobius-strip.pdf_tex │ ├── mobius-strip.svg │ ├── not-a-foliation-example.pdf │ ├── not-a-foliation-example.pdf_tex │ ├── not-a-foliation-example.svg │ ├── not-hausdorff-example.pdf │ ├── not-hausdorff-example.pdf_tex │ ├── not-hausdorff-example.svg │ ├── orientation-of-boundary.pdf │ ├── orientation-of-boundary.pdf_tex │ ├── orientation-of-boundary.svg │ ├── proofsubmersion.pdf │ ├── proofsubmersion.pdf_tex │ ├── proofsubmersion.svg │ ├── rham-cohomology-definition.pdf │ ├── rham-cohomology-definition.pdf_tex │ ├── rham-cohomology-definition.svg │ ├── rham-cohomology.pdf │ ├── rham-cohomology.pdf_tex │ ├── rham-cohomology.svg │ ├── smooth-function-from-m-to-n.pdf │ ├── smooth-function-from-m-to-n.pdf_tex │ ├── smooth-function-from-m-to-n.svg │ ├── smooth-function-to-r.pdf │ ├── smooth-function-to-r.pdf_tex │ ├── smooth-function-to-r.svg │ ├── submanifold-torus-example.pdf │ ├── submanifold-torus-example.pdf_tex │ ├── submanifold-torus-example.svg │ ├── submanifold.pdf │ ├── submanifold.pdf_tex │ ├── submanifold.svg │ ├── submersion-theorem.pdf │ ├── submersion-theorem.pdf_tex │ ├── submersion-theorem.svg │ ├── tangent-vector-definition-chart-independent-ForDiffForms.pdf │ ├── tangent-vector-definition-chart-independent-ForDiffForms.pdf_tex │ ├── tangent-vector-definition-chart-independent-ForDiffForms.svg │ ├── tangent-vector-definition-chart-independent.pdf │ ├── tangent-vector-definition-chart-independent.pdf_tex │ ├── tangent-vector-definition-chart-independent.svg │ ├── vector-bundle-definition.pdf │ ├── vector-bundle-definition.pdf_tex │ └── vector-bundle-definition.svg ├── les_01.tex ├── les_02.tex ├── les_03.tex ├── les_04.tex ├── les_05.tex ├── les_06.tex ├── les_07.tex ├── les_08.tex ├── les_09.tex ├── les_10.tex ├── les_11.tex ├── les_12.tex ├── les_13.tex ├── master.tex └── preamble.tex └── group-theory ├── figures ├── diagram.pdf ├── diagram.pdf_tex └── diagram.svg ├── les_01.tex ├── les_02.tex ├── les_03.tex ├── les_04.tex ├── les_05.tex ├── les_06.tex ├── les_07.tex ├── les_08.tex ├── les_09.tex ├── les_10.tex ├── les_11.tex ├── les_12.tex ├── les_13.tex ├── les_14.tex ├── les_15.tex ├── les_16.tex ├── les_17.tex ├── les_18.tex ├── les_19.tex ├── les_20.tex ├── les_21.tex ├── les_22.tex ├── master.tex └── preamble.tex /README.md: -------------------------------------------------------------------------------- 1 | # LaTeX code for some of my lecture notes 2 | 3 | ## Algebraic topology 4 | 5 | ![Colorful notes](https://user-images.githubusercontent.com/7069691/159117292-d0c03dfa-7a85-450f-a625-74433c3673a3.png) 6 | 7 | ## Differential geometry 8 | 9 | ![Black and white](https://user-images.githubusercontent.com/7069691/159117366-87d83ed5-8910-4700-bb59-760aeb0c98a5.png) 10 | 11 | ## Group theory 12 | 13 | ![Group theory](https://user-images.githubusercontent.com/7069691/159118002-a9459ac7-9a21-48a0-b992-7d8e1d49d6b4.png) 14 | 15 | 16 | ## [Master's thesis](https://github.com/gillescastel/masterthesis) 17 | 18 | ![2021_10_04_001](https://user-images.githubusercontent.com/7069691/135912959-b73f2080-ad53-40d3-bd45-ee54fac604d0.png) 19 | -------------------------------------------------------------------------------- /algebraic-topology/figures/antipode-preserving-maps.pdf: -------------------------------------------------------------------------------- https://raw.githubusercontent.com/gillescastel/lecture-notes/929672a96abc27eaeb6fa58b1d277b3582d28532/algebraic-topology/figures/antipode-preserving-maps.pdf -------------------------------------------------------------------------------- /algebraic-topology/figures/base-case-of-theorem.pdf: -------------------------------------------------------------------------------- https://raw.githubusercontent.com/gillescastel/lecture-notes/929672a96abc27eaeb6fa58b1d277b3582d28532/algebraic-topology/figures/base-case-of-theorem.pdf -------------------------------------------------------------------------------- /algebraic-topology/figures/base-case-of-theorem.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 'base-case-of-theorem.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 | 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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 | 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image file 'covering-space-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 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Engelen, 2010 3 | %% Accompanies image file 'definition-of-suspension-general.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}{641.50506448bp}% 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}(1,0.3180705)% 54 | \lineheight{1}% 55 | \setlength\tabcolsep{0pt}% 56 | 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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}{561.16693452bp}% 42 | \ifx\svgscale\undefined% 43 | \relax% 44 | \else% 45 | \setlength{\unitlength}{\unitlength * \real{\svgscale}}% 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\put(0,0){\includegraphics[width=\unitlength,page=5]{definition-of-suspension.pdf}}% 70 | \end{picture}% 71 | \endgroup% 72 | -------------------------------------------------------------------------------- /algebraic-topology/figures/definition-singular-p-simplex.pdf: -------------------------------------------------------------------------------- https://raw.githubusercontent.com/gillescastel/lecture-notes/929672a96abc27eaeb6fa58b1d277b3582d28532/algebraic-topology/figures/definition-singular-p-simplex.pdf -------------------------------------------------------------------------------- /algebraic-topology/figures/definition-singular-p-simplex.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-singular-p-simplex.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}{568.78746694bp}% 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}(1,0.32835115)% 54 | \lineheight{1}% 55 | \setlength\tabcolsep{0pt}% 56 | \put(0,0){\includegraphics[width=\unitlength,page=1]{definition-singular-p-simplex.pdf}}% 57 | \put(0.43800087,0.2451716){\color[rgb]{0,0,0}\makebox(0,0)[lt]{\lineheight{1.25}\smash{\begin{tabular}[t]{l}$\phi$\end{tabular}}}}% 58 | \put(0,0){\includegraphics[width=\unitlength,page=2]{definition-singular-p-simplex.pdf}}% 59 | \end{picture}% 60 | \endgroup% 61 | -------------------------------------------------------------------------------- /algebraic-topology/figures/deformation-rectract-example-2.pdf: -------------------------------------------------------------------------------- https://raw.githubusercontent.com/gillescastel/lecture-notes/929672a96abc27eaeb6fa58b1d277b3582d28532/algebraic-topology/figures/deformation-rectract-example-2.pdf -------------------------------------------------------------------------------- /algebraic-topology/figures/deformation-rectract-example-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 'deformation-rectract-example-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}{377.18469334bp}% 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}(1,0.27612078)% 54 | \lineheight{1}% 55 | \setlength\tabcolsep{0pt}% 56 | \put(0,0){\includegraphics[width=\unitlength,page=1]{deformation-rectract-example-2.pdf}}% 57 | \put(0.73112916,0.2218212){\color[rgb]{0,0,0}\makebox(0,0)[lt]{\lineheight{1.25}\smash{\begin{tabular}[t]{l}$A$\end{tabular}}}}% 58 | \end{picture}% 59 | \endgroup% 60 | -------------------------------------------------------------------------------- /algebraic-topology/figures/deformation-rectract-example-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 | 84 | $A$ 95 | 96 | 97 | -------------------------------------------------------------------------------- /algebraic-topology/figures/deformation-retract-example.pdf: -------------------------------------------------------------------------------- https://raw.githubusercontent.com/gillescastel/lecture-notes/929672a96abc27eaeb6fa58b1d277b3582d28532/algebraic-topology/figures/deformation-retract-example.pdf -------------------------------------------------------------------------------- /algebraic-topology/figures/deformation-retract-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 'deformation-retract-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 | 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-------------------------------------------------------------------------------- 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 'dependence-of-base-point.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}{370.35452775bp}% 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 | 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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}{295.56825653bp}% 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 | 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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 | 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PDF/EPS/PS + LaTeX output extension by Johan Engelen, 2010 3 | %% Accompanies image file 'lemma-universal-covering-space.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 | 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LaTeX output extension by Johan Engelen, 2010 3 | %% Accompanies image file 'lift-of-a-path-homotopy.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 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/algebraic-topology/figures/lift-of-path-homotopy-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 'lift-of-path-homotopy-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}{491.07545868bp}% 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 | 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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 | 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'no-antipodal-preserving-map-from-s2-to-s1.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}{1045.77949103bp}% 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}(1,0.27877395)% 54 | \lineheight{1}% 55 | \setlength\tabcolsep{0pt}% 56 | \put(0,0){\includegraphics[width=\unitlength,page=1]{no-antipodal-preserving-map-from-s2-to-s1.pdf}}% 57 | 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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 | 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\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}{524.12882167bp}% 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}(1,0.28160512)% 54 | \lineheight{1}% 55 | \setlength\tabcolsep{0pt}% 56 | \put(0,0){\includegraphics[width=\unitlength,page=1]{proof-fixed-point-brouwer.pdf}}% 57 | \put(0.48201599,0.16441523){\color[rgb]{0,0,0}\makebox(0,0)[lt]{\lineheight{1.25}\smash{\begin{tabular}[t]{l}$x$\end{tabular}}}}% 58 | \put(0.49824914,0.20260936){\color[rgb]{0,0,0}\makebox(0,0)[lt]{\lineheight{1.25}\smash{\begin{tabular}[t]{l}$f(x)$\end{tabular}}}}% 59 | 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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}{589.05992403bp}% 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}(1,0.45948048)% 54 | \lineheight{1}% 55 | \setlength\tabcolsep{0pt}% 56 | \put(0,0){\includegraphics[width=\unitlength,page=1]{proof-path.pdf}}% 57 | \put(0.2100692,0.40918148){\color[rgb]{0,0,0}\makebox(0,0)[lt]{\lineheight{1.25}\smash{\begin{tabular}[t]{l}$1$\end{tabular}}}}% 58 | \put(0.22604228,0.06452911){\color[rgb]{0,0,0}\makebox(0,0)[lt]{\lineheight{1.25}\smash{\begin{tabular}[t]{l}$0$\end{tabular}}}}% 59 | \put(0.64165909,0.05168706){\color[rgb]{0,0,0}\makebox(0,0)[lt]{\lineheight{1.25}\smash{\begin{tabular}[t]{l}$1$\end{tabular}}}}% 60 | \put(0.50475853,0.0520166){\color[rgb]{0,0,0}\makebox(0,0)[lt]{\lineheight{1.25}\smash{\begin{tabular}[t]{l}$b$\end{tabular}}}}% 61 | \put(0.35128796,0.05234615){\color[rgb]{0,0,0}\makebox(0,0)[lt]{\lineheight{1.25}\smash{\begin{tabular}[t]{l}$a$\end{tabular}}}}% 62 | \put(0.22213662,0.21166731){\color[rgb]{0,0,0}\makebox(0,0)[lt]{\lineheight{1.25}\smash{\begin{tabular}[t]{l}$c$\end{tabular}}}}% 63 | \put(0.22191693,0.3015485){\color[rgb]{0,0,0}\makebox(0,0)[lt]{\lineheight{1.25}\smash{\begin{tabular}[t]{l}$d$\end{tabular}}}}% 64 | \put(0,0){\includegraphics[width=\unitlength,page=2]{proof-path.pdf}}% 65 | \end{picture}% 66 | \endgroup% 67 | -------------------------------------------------------------------------------- /algebraic-topology/figures/proof-prop-123.pdf: -------------------------------------------------------------------------------- https://raw.githubusercontent.com/gillescastel/lecture-notes/929672a96abc27eaeb6fa58b1d277b3582d28532/algebraic-topology/figures/proof-prop-123.pdf -------------------------------------------------------------------------------- /algebraic-topology/figures/proof-prop-123.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-prop-123.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]{proof-prop-123.pdf}}% 57 | \put(0.49811039,0.35799567){\color[rgb]{0,0,0}\makebox(0,0)[lt]{\lineheight{1.25}\smash{\begin{tabular}[t]{l}$f(x)$\end{tabular}}}}% 58 | \put(0.19275277,0.17916552){\color[rgb]{0,0,0}\makebox(0,0)[lt]{\lineheight{1.25}\smash{\begin{tabular}[t]{l}$A g(x)$\end{tabular}}}}% 59 | \put(0,0){\includegraphics[width=\unitlength,page=2]{proof-prop-123.pdf}}% 60 | \put(0.26214434,0.33620904){\color[rgb]{0,0,0}\makebox(0,0)[lt]{\lineheight{1.25}\smash{\begin{tabular}[t]{l}$S^{n}$\end{tabular}}}}% 61 | \put(0,0){\includegraphics[width=\unitlength,page=3]{proof-prop-123.pdf}}% 62 | \end{picture}% 63 | \endgroup% 64 | -------------------------------------------------------------------------------- /algebraic-topology/figures/testfiguur.pdf: -------------------------------------------------------------------------------- https://raw.githubusercontent.com/gillescastel/lecture-notes/929672a96abc27eaeb6fa58b1d277b3582d28532/algebraic-topology/figures/testfiguur.pdf -------------------------------------------------------------------------------- /algebraic-topology/figures/testfiguur.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 'testfiguur.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]{testfiguur.pdf}}% 57 | \put(0.0875686,0.39671618){\color[rgb]{0,0,0}\makebox(0,0)[lt]{\lineheight{1.25}\smash{\begin{tabular}[t]{l}$\int_{-\infty}^{\infty} e^{-x^2}dx = \sqrt{\pi} $\end{tabular}}}}% 58 | \end{picture}% 59 | \endgroup% 60 | -------------------------------------------------------------------------------- /algebraic-topology/figures/testfiguur.svg: -------------------------------------------------------------------------------- 1 | 2 | 3 | 4 | 19 | 21 | 43 | 51 | 52 | 54 | 55 | 57 | image/svg+xml 58 | 60 | 61 | 62 | 63 | 64 | 69 | 74 | $\int_{-\infty}^{\infty} e^{-x^2}dx = \sqrt{\pi} $ 85 | 86 | 87 | -------------------------------------------------------------------------------- /algebraic-topology/figures/theorem-59-1.pdf: -------------------------------------------------------------------------------- https://raw.githubusercontent.com/gillescastel/lecture-notes/929672a96abc27eaeb6fa58b1d277b3582d28532/algebraic-topology/figures/theorem-59-1.pdf 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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}{559.3286277bp}% 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}(1,0.56519521)% 54 | \lineheight{1}% 55 | \setlength\tabcolsep{0pt}% 56 | \put(0,0){\includegraphics[width=\unitlength,page=1]{torus-covering.pdf}}% 57 | \put(0.33902841,0.07091048){\color[rgb]{0,0,0}\makebox(0,0)[lt]{\lineheight{1.25}\smash{\begin{tabular}[t]{l}$(1, 1)$\end{tabular}}}}% 58 | \put(0.33808783,0.03322105){\color[rgb]{0,0,0}\makebox(0,0)[lt]{\lineheight{1.25}\smash{\begin{tabular}[t]{l}$B_0 = S^{1} \times \{1\} \cup \{1\} \times S^{1}$\end{tabular}}}}% 59 | \put(0,0){\includegraphics[width=\unitlength,page=2]{torus-covering.pdf}}% 60 | \end{picture}% 61 | \endgroup% 62 | -------------------------------------------------------------------------------- /algebraic-topology/figures/tweeling-zwemband.pdf: -------------------------------------------------------------------------------- https://raw.githubusercontent.com/gillescastel/lecture-notes/929672a96abc27eaeb6fa58b1d277b3582d28532/algebraic-topology/figures/tweeling-zwemband.pdf -------------------------------------------------------------------------------- /algebraic-topology/figures/tweeling-zwemband.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 'tweeling-zwemband.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}{932.68493172bp}% 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}(1,0.16544249)% 54 | \lineheight{1}% 55 | \setlength\tabcolsep{0pt}% 56 | \put(0,0){\includegraphics[width=\unitlength,page=1]{tweeling-zwemband.pdf}}% 57 | \end{picture}% 58 | \endgroup% 59 | -------------------------------------------------------------------------------- /algebraic-topology/figures/wedge-circles.pdf: -------------------------------------------------------------------------------- https://raw.githubusercontent.com/gillescastel/lecture-notes/929672a96abc27eaeb6fa58b1d277b3582d28532/algebraic-topology/figures/wedge-circles.pdf -------------------------------------------------------------------------------- /algebraic-topology/figures/wedge-circles.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 'wedge-circles.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}{695.0563638bp}% 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}(1,0.40099475)% 54 | \lineheight{1}% 55 | \setlength\tabcolsep{0pt}% 56 | \put(0,0){\includegraphics[width=\unitlength,page=1]{wedge-circles.pdf}}% 57 | \end{picture}% 58 | \endgroup% 59 | -------------------------------------------------------------------------------- /algebraic-topology/figures/well-defined-general-lifting-lemma.pdf: -------------------------------------------------------------------------------- https://raw.githubusercontent.com/gillescastel/lecture-notes/929672a96abc27eaeb6fa58b1d277b3582d28532/algebraic-topology/figures/well-defined-general-lifting-lemma.pdf -------------------------------------------------------------------------------- /algebraic-topology/les_08.tex: -------------------------------------------------------------------------------- 1 | \lesson{8}{di 03 dec 2019 23:02}{Ill} 2 | -------------------------------------------------------------------------------- /algebraic-topology/master.tex: -------------------------------------------------------------------------------- 1 | \documentclass[a4paper]{report} 2 | \input{./preamble.tex} 3 | % \usepackage{cmbright} 4 | 5 | \usepackage{faktor} 6 | 7 | \makeatletter 8 | \DeclareRobustCommand*{\mfaktor}[3][] 9 | { 10 | { \mathpalette{\mfaktor@impl@}{{#1}{#2}{#3}} } 11 | } 12 | \newcommand*{\mfaktor@impl@}[2]{\mfaktor@impl#1#2} 13 | \newcommand*{\mfaktor@impl}[4]{ 14 | \settoheight{\faktor@zaehlerhoehe}{\ensuremath{#1#2{#3}}}% 15 | \settoheight{\faktor@nennerhoehe}{\ensuremath{#1#2{#4}}}% 16 | \raisebox{-0.5\faktor@zaehlerhoehe}{\ensuremath{#1#2{#3}}}% 17 | \mkern-4mu\diagdown\mkern-5mu% 18 | \raisebox{0.5\faktor@nennerhoehe}{\ensuremath{#1#2{#4}}}% 19 | } 20 | \makeatother 21 | 22 | \DeclareMathOperator{\Ker}{ker} 23 | \DeclareMathOperator{\im}{Im} 24 | 25 | \title{Algebraic Topology} 26 | \begin{document} 27 | \maketitle 28 | \tableofcontents 29 | % start lessons 30 | \input{les_01.tex} 31 | \input{les_02.tex} 32 | \input{les_03.tex} 33 | \input{les_04.tex} 34 | \input{les_05.tex} 35 | \input{les_06.tex} 36 | \input{les_07.tex} 37 | \input{les_08.tex} 38 | \input{les_09.tex} 39 | \input{les_10.tex} 40 | % end lessons 41 | \end{document} 42 | -------------------------------------------------------------------------------- /differential-geometry/figures/GregoryvanKruijsdijk.pdf: 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/differential-geometry/figures/definition-of-a-section.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-of-a-section.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}{502.36806314bp}% 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}(1,0.46551018)% 54 | \lineheight{1}% 55 | \setlength\tabcolsep{0pt}% 56 | \put(0,0){\includegraphics[width=\unitlength,page=1]{definition-of-a-section.pdf}}% 57 | \put(0.53909241,0.08208121){\color[rgb]{0,0,0}\makebox(0,0)[lt]{\lineheight{1.25}\smash{\begin{tabular}[t]{l}$B = S^1$\end{tabular}}}}% 58 | \put(0,0){\includegraphics[width=\unitlength,page=2]{definition-of-a-section.pdf}}% 59 | \put(0.55396786,0.36137651){\color[rgb]{0,0,0}\makebox(0,0)[lt]{\lineheight{1.25}\smash{\begin{tabular}[t]{l}$E = S^1 \times (-\epsilon, \epsilon)$\end{tabular}}}}% 60 | \put(0,0){\includegraphics[width=\unitlength,page=3]{definition-of-a-section.pdf}}% 61 | \put(0.40238276,0.1781068){\color[rgb]{0,0,0}\makebox(0,0)[lt]{\lineheight{1.25}\smash{\begin{tabular}[t]{l}$\pi$\end{tabular}}}}% 62 | \put(0,0){\includegraphics[width=\unitlength,page=4]{definition-of-a-section.pdf}}% 63 | \put(0.26547346,0.32984086){\color[rgb]{0,0,0}\makebox(0,0)[lt]{\lineheight{1.25}\smash{\begin{tabular}[t]{l}Image of a section\end{tabular}}}}% 64 | \end{picture}% 65 | \endgroup% 66 | -------------------------------------------------------------------------------- /differential-geometry/figures/definition-of-foliation.pdf: -------------------------------------------------------------------------------- https://raw.githubusercontent.com/gillescastel/lecture-notes/929672a96abc27eaeb6fa58b1d277b3582d28532/differential-geometry/figures/definition-of-foliation.pdf -------------------------------------------------------------------------------- /differential-geometry/figures/definition-of-foliation.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-of-foliation.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}{507.74997982bp}% 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}(1,0.48005912)% 54 | \lineheight{1}% 55 | \setlength\tabcolsep{0pt}% 56 | \put(0,0){\includegraphics[width=\unitlength,page=1]{definition-of-foliation.pdf}}% 57 | \put(0.50138504,0.41072708){\color[rgb]{0,0,0}\makebox(0,0)[lt]{\lineheight{1.25}\smash{\begin{tabular}[t]{l}$\R^{n-k}$\end{tabular}}}}% 58 | \put(0.77329945,0.24287001){\color[rgb]{0,0,0}\makebox(0,0)[lt]{\lineheight{1.25}\smash{\begin{tabular}[t]{l}$\R^{k}$\end{tabular}}}}% 59 | \put(0,0){\includegraphics[width=\unitlength,page=2]{definition-of-foliation.pdf}}% 60 | \put(0.44318293,0.33408128){\color[rgb]{0,0,0}\makebox(0,0)[lt]{\lineheight{1.25}\smash{\begin{tabular}[t]{l}$\phi$\end{tabular}}}}% 61 | \put(0.31770307,0.29557834){\color[rgb]{0,0,0}\makebox(0,0)[lt]{\lineheight{1.25}\smash{\begin{tabular}[t]{l}$M$\end{tabular}}}}% 62 | \put(0,0){\includegraphics[width=\unitlength,page=3]{definition-of-foliation.pdf}}% 63 | \end{picture}% 64 | \endgroup% 65 | -------------------------------------------------------------------------------- /differential-geometry/figures/example-of-a-vector-bundle-that-doesnt-admit-a-frame.pdf: 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\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}{732.01428511bp}% 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}(1,0.31377548)% 54 | \lineheight{1}% 55 | \setlength\tabcolsep{0pt}% 56 | \put(0,0){\includegraphics[width=\unitlength,page=1]{example-of-a-vector-bundle-that-doesnt-admit-a-frame.pdf}}% 57 | \put(0.60673972,0.29731469){\color[rgb]{0,0,0}\makebox(0,0)[lt]{\lineheight{1.25}\smash{\begin{tabular}[t]{l}$S^{2}$\end{tabular}}}}% 58 | \put(0,0){\includegraphics[width=\unitlength,page=2]{example-of-a-vector-bundle-that-doesnt-admit-a-frame.pdf}}% 59 | \end{picture}% 60 | \endgroup% 61 | -------------------------------------------------------------------------------- /differential-geometry/figures/example-of-fiber-bundle.pdf: -------------------------------------------------------------------------------- https://raw.githubusercontent.com/gillescastel/lecture-notes/929672a96abc27eaeb6fa58b1d277b3582d28532/differential-geometry/figures/example-of-fiber-bundle.pdf -------------------------------------------------------------------------------- /differential-geometry/figures/example-of-fiber-bundle.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-of-fiber-bundle.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}{546.11423763bp}% 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}(1,0.381263)% 54 | \lineheight{1}% 55 | \setlength\tabcolsep{0pt}% 56 | \put(0,0){\includegraphics[width=\unitlength,page=1]{example-of-fiber-bundle.pdf}}% 57 | \put(0.60058316,0.04104748){\color[rgb]{0,0,0}\makebox(0,0)[lt]{\lineheight{1.25}\smash{\begin{tabular}[t]{l}$B = S^1$\end{tabular}}}}% 58 | \put(0,0){\includegraphics[width=\unitlength,page=2]{example-of-fiber-bundle.pdf}}% 59 | \put(0.61426698,0.2979699){\color[rgb]{0,0,0}\makebox(0,0)[lt]{\lineheight{1.25}\smash{\begin{tabular}[t]{l}$E = S^1 \times (-\epsilon, \epsilon)$\end{tabular}}}}% 60 | \put(0,0){\includegraphics[width=\unitlength,page=3]{example-of-fiber-bundle.pdf}}% 61 | \put(0.47482448,0.12938092){\color[rgb]{0,0,0}\makebox(0,0)[lt]{\lineheight{1.25}\smash{\begin{tabular}[t]{l}$\pi$\end{tabular}}}}% 62 | \put(0,0){\includegraphics[width=\unitlength,page=4]{example-of-fiber-bundle.pdf}}% 63 | \put(0.5318632,0.16797891){\color[rgb]{0,0,0}\makebox(0,0)[lt]{\lineheight{1.25}\smash{\begin{tabular}[t]{l}$\pi^{-1}(U)$\end{tabular}}}}% 64 | \put(0.54959471,-0.00307587){\color[rgb]{0,0,0}\makebox(0,0)[lt]{\lineheight{1.25}\smash{\begin{tabular}[t]{l}$U$\end{tabular}}}}% 65 | \put(0,0){\includegraphics[width=\unitlength,page=5]{example-of-fiber-bundle.pdf}}% 66 | \end{picture}% 67 | \endgroup% 68 | -------------------------------------------------------------------------------- /differential-geometry/figures/example-submersion.pdf: -------------------------------------------------------------------------------- https://raw.githubusercontent.com/gillescastel/lecture-notes/929672a96abc27eaeb6fa58b1d277b3582d28532/differential-geometry/figures/example-submersion.pdf -------------------------------------------------------------------------------- /differential-geometry/figures/example-submersion.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-submersion.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}{342.86660502bp}% 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}(1,0.37965182)% 54 | \lineheight{1}% 55 | \setlength\tabcolsep{0pt}% 56 | \put(0,0){\includegraphics[width=\unitlength,page=1]{example-submersion.pdf}}% 57 | \end{picture}% 58 | \endgroup% 59 | -------------------------------------------------------------------------------- /differential-geometry/figures/f-related.pdf: -------------------------------------------------------------------------------- https://raw.githubusercontent.com/gillescastel/lecture-notes/929672a96abc27eaeb6fa58b1d277b3582d28532/differential-geometry/figures/f-related.pdf -------------------------------------------------------------------------------- /differential-geometry/figures/f-related.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 'f-related.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}{395.41676439bp}% 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}(1,0.64711075)% 54 | \lineheight{1}% 55 | \setlength\tabcolsep{0pt}% 56 | \put(0,0){\includegraphics[width=\unitlength,page=1]{f-related.pdf}}% 57 | \put(0.55254769,0.13897981){\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]{f-related.pdf}}% 59 | \end{picture}% 60 | \endgroup% 61 | -------------------------------------------------------------------------------- /differential-geometry/figures/figure-1.pdf: -------------------------------------------------------------------------------- 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\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}{414.1379433bp}% 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}(1,0.56808762)% 54 | \lineheight{1}% 55 | \setlength\tabcolsep{0pt}% 56 | \put(0,0){\includegraphics[width=\unitlength,page=1]{figure-1.pdf}}% 57 | \put(0.08737998,0.11117292){\color[rgb]{0,0,0}\makebox(0,0)[lt]{\lineheight{1.25}\smash{\begin{tabular}[t]{l}$\mathbb R^{n}$\end{tabular}}}}% 58 | \put(0,0){\includegraphics[width=\unitlength,page=2]{figure-1.pdf}}% 59 | \put(0.31791586,0.30863711){\color[rgb]{0,0,0}\makebox(0,0)[lt]{\lineheight{1.25}\smash{\begin{tabular}[t]{l}$\phi$\end{tabular}}}}% 60 | \put(0,0){\includegraphics[width=\unitlength,page=3]{figure-1.pdf}}% 61 | \put(0.68345979,0.51132864){\color[rgb]{0,0,0}\makebox(0,0)[lt]{\lineheight{1.25}\smash{\begin{tabular}[t]{l}$\left.\dfrac{\partial}{\partial x^i}\right|_p $ is basis of $T_{p}U$\end{tabular}}}}% 62 | \put(0.2730544,0.14291826){\color[rgb]{0,0,0}\makebox(0,0)[lt]{\lineheight{1.25}\smash{\begin{tabular}[t]{l}Basis of $T_{\phi(p)}\phi(U)$\end{tabular}}}}% 63 | \put(0,0){\includegraphics[width=\unitlength,page=4]{figure-1.pdf}}% 64 | \end{picture}% 65 | \endgroup% 66 | -------------------------------------------------------------------------------- /differential-geometry/figures/homotopy-definition.pdf: -------------------------------------------------------------------------------- https://raw.githubusercontent.com/gillescastel/lecture-notes/929672a96abc27eaeb6fa58b1d277b3582d28532/differential-geometry/figures/homotopy-definition.pdf -------------------------------------------------------------------------------- /differential-geometry/figures/homotopy-definition.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 'homotopy-definition.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}{457.31265571bp}% 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 | 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/differential-geometry/figures/interpretation-of-lie-bracket-lemma-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 'interpretation-of-lie-bracket-lemma-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}{241.0186287bp}% 42 | \ifx\svgscale\undefined% 43 | \relax% 44 | \else% 45 | \setlength{\unitlength}{\unitlength * \real{\svgscale}}% 46 | \fi% 47 | \else% 48 | 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-------------------------------------------------------------------------------- /differential-geometry/figures/mobius-strip.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 'mobius-strip.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}{413.96769847bp}% 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}(1,0.17454401)% 54 | \lineheight{1}% 55 | \setlength\tabcolsep{0pt}% 56 | \put(0.50469131,0.06131937){\color[rgb]{0,0,0}\makebox(0,0)[lt]{\lineheight{1.25}\smash{\begin{tabular}[t]{l}=\end{tabular}}}}% 57 | \put(0,0){\includegraphics[width=\unitlength,page=1]{mobius-strip.pdf}}% 58 | \end{picture}% 59 | \endgroup% 60 | -------------------------------------------------------------------------------- /differential-geometry/figures/not-a-foliation-example.pdf: -------------------------------------------------------------------------------- https://raw.githubusercontent.com/gillescastel/lecture-notes/929672a96abc27eaeb6fa58b1d277b3582d28532/differential-geometry/figures/not-a-foliation-example.pdf -------------------------------------------------------------------------------- /differential-geometry/figures/not-a-foliation-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 'not-a-foliation-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}{666.03891928bp}% 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 | 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extension by Johan Engelen, 2010 3 | %% Accompanies image file 'not-hausdorff-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}{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 | 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/differential-geometry/figures/orientation-of-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 'orientation-of-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}{528.36850624bp}% 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}(1,0.36190971)% 54 | \lineheight{1}% 55 | \setlength\tabcolsep{0pt}% 56 | \put(0,0){\includegraphics[width=\unitlength,page=1]{orientation-of-boundary.pdf}}% 57 | \put(0.59636177,0.30876866){\color[rgb]{0,0,0}\makebox(0,0)[lt]{\lineheight{1.25}\smash{\begin{tabular}[t]{l}$v_1$\end{tabular}}}}% 58 | \put(0.66812197,0.25394){\color[rgb]{0,0,0}\makebox(0,0)[lt]{\lineheight{1.25}\smash{\begin{tabular}[t]{l}$e$\end{tabular}}}}% 59 | \put(0,0){\includegraphics[width=\unitlength,page=2]{orientation-of-boundary.pdf}}% 60 | \end{picture}% 61 | \endgroup% 62 | -------------------------------------------------------------------------------- /differential-geometry/figures/proofsubmersion.pdf: -------------------------------------------------------------------------------- https://raw.githubusercontent.com/gillescastel/lecture-notes/929672a96abc27eaeb6fa58b1d277b3582d28532/differential-geometry/figures/proofsubmersion.pdf -------------------------------------------------------------------------------- /differential-geometry/figures/proofsubmersion.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 'proofsubmersion.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}{321.26471572bp}% 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}(1,0.27333851)% 54 | \lineheight{1}% 55 | \setlength\tabcolsep{0pt}% 56 | \put(0,0){\includegraphics[width=\unitlength,page=1]{proofsubmersion.pdf}}% 57 | \put(0.63750846,0.19317768){\color[rgb]{0,0,0}\makebox(0,0)[lt]{\lineheight{1.25}\smash{\begin{tabular}[t]{l}$\pi$\end{tabular}}}}% 58 | \put(0,0){\includegraphics[width=\unitlength,page=2]{proofsubmersion.pdf}}% 59 | \put(0.25871295,0.00512583){\color[rgb]{0,0,0}\makebox(0,0)[lt]{\lineheight{1.25}\smash{\begin{tabular}[t]{l}$(\tau \circ \phi_M) (f^{-1}(c) \cap U)$\end{tabular}}}}% 60 | 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| %% 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 | 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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}{553.25855165bp}% 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}(1,0.29791347)% 54 | \lineheight{1}% 55 | \setlength\tabcolsep{0pt}% 56 | \put(0,0){\includegraphics[width=\unitlength,page=1]{rham-cohomology.pdf}}% 57 | 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-------------------------------------------------------------------------------- /differential-geometry/figures/smooth-function-to-r.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 'smooth-function-to-r.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}{491.30063515bp}% 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}(1,0.56283507)% 54 | \lineheight{1}% 55 | \setlength\tabcolsep{0pt}% 56 | \put(0,0){\includegraphics[width=\unitlength,page=1]{smooth-function-to-r.pdf}}% 57 | \put(0.28483122,0.40217332){\color[rgb]{0,0,0}\makebox(0,0)[lt]{\lineheight{1.25}\smash{\begin{tabular}[t]{l}$p$\end{tabular}}}}% 58 | \put(0.23119012,0.47250868){\color[rgb]{0,0,0}\makebox(0,0)[lt]{\lineheight{1.25}\smash{\begin{tabular}[t]{l}$M$\end{tabular}}}}% 59 | \put(0,0){\includegraphics[width=\unitlength,page=2]{smooth-function-to-r.pdf}}% 60 | \put(0.59458905,0.4451573){\color[rgb]{0,0,0}\makebox(0,0)[lt]{\lineheight{1.25}\smash{\begin{tabular}[t]{l}$f$\end{tabular}}}}% 61 | \put(0.74018371,0.42179502){\color[rgb]{0,0,0}\makebox(0,0)[lt]{\lineheight{1.25}\smash{\begin{tabular}[t]{l}$\mathbb R$\end{tabular}}}}% 62 | 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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 | 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https://raw.githubusercontent.com/gillescastel/lecture-notes/929672a96abc27eaeb6fa58b1d277b3582d28532/differential-geometry/figures/submanifold.pdf -------------------------------------------------------------------------------- /differential-geometry/figures/submanifold.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 'submanifold.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}{459.39720334bp}% 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}(1,0.33342465)% 54 | \lineheight{1}% 55 | \setlength\tabcolsep{0pt}% 56 | \put(0.15775166,0.30970687){\color[rgb]{0,0,0}\makebox(0,0)[lt]{\lineheight{1.25}\smash{\begin{tabular}[t]{l}$N$\end{tabular}}}}% 57 | \put(0,0){\includegraphics[width=\unitlength,page=1]{submanifold.pdf}}% 58 | \put(0.31706274,0.24721861){\color[rgb]{0,0,0}\makebox(0,0)[lt]{\lineheight{1.25}\smash{\begin{tabular}[t]{l}$M$\end{tabular}}}}% 59 | \put(0,0){\includegraphics[width=\unitlength,page=2]{submanifold.pdf}}% 60 | \put(0.24978134,0.23649129){\color[rgb]{0,0,0}\makebox(0,0)[lt]{\lineheight{1.25}\smash{\begin{tabular}[t]{l}$p$\end{tabular}}}}% 61 | \put(0,0){\includegraphics[width=\unitlength,page=3]{submanifold.pdf}}% 62 | \put(0.52364106,0.22404606){\color[rgb]{0,0,0}\makebox(0,0)[lt]{\lineheight{1.25}\smash{\begin{tabular}[t]{l}$\phi$\end{tabular}}}}% 63 | \put(0,0){\includegraphics[width=\unitlength,page=4]{submanifold.pdf}}% 64 | \put(0.67045798,0.15701757){\color[rgb]{0,0,0}\makebox(0,0)[lt]{\lineheight{1.25}\smash{\begin{tabular}[t]{l}$\mathbb R^{n}$\end{tabular}}}}% 65 | \put(0.81103448,0.14523365){\color[rgb]{0,0,0}\makebox(0,0)[lt]{\lineheight{1.25}\smash{\begin{tabular}[t]{l}$\phi(U)$\end{tabular}}}}% 66 | \put(0,0){\includegraphics[width=\unitlength,page=5]{submanifold.pdf}}% 67 | \put(0.89700343,0.07898124){\color[rgb]{0,0,0}\makebox(0,0)[lt]{\lineheight{1.25}\smash{\begin{tabular}[t]{l}$\R^{m} \times \{0\} $\end{tabular}}}}% 68 | \put(0.71649049,0.23745682){\color[rgb]{0,0,0}\makebox(0,0)[lt]{\lineheight{1.25}\smash{\begin{tabular}[t]{l}$\{0\} \times \R^{n-m}$\end{tabular}}}}% 69 | \put(0,0){\includegraphics[width=\unitlength,page=6]{submanifold.pdf}}% 70 | \end{picture}% 71 | \endgroup% 72 | -------------------------------------------------------------------------------- /differential-geometry/figures/submersion-theorem.pdf: -------------------------------------------------------------------------------- https://raw.githubusercontent.com/gillescastel/lecture-notes/929672a96abc27eaeb6fa58b1d277b3582d28532/differential-geometry/figures/submersion-theorem.pdf -------------------------------------------------------------------------------- /differential-geometry/figures/submersion-theorem.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 'submersion-theorem.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}{480.85120975bp}% 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}(1,0.45414145)% 54 | \lineheight{1}% 55 | \setlength\tabcolsep{0pt}% 56 | \put(0,0){\includegraphics[width=\unitlength,page=1]{submersion-theorem.pdf}}% 57 | \put(0.41243973,0.06656507){\color[rgb]{0,0,0}\makebox(0,0)[lt]{\lineheight{1.25}\smash{\begin{tabular}[t]{l}$\R^n$\end{tabular}}}}% 58 | \put(0,0){\includegraphics[width=\unitlength,page=2]{submersion-theorem.pdf}}% 59 | \put(0.24168441,0.09924551){\color[rgb]{0,0,0}\makebox(0,0)[lt]{\lineheight{1.25}\smash{\begin{tabular}[t]{l}$f$\end{tabular}}}}% 60 | \put(0.4060619,0.39154255){\color[rgb]{0,0,0}\makebox(0,0)[lt]{\lineheight{1.25}\smash{\begin{tabular}[t]{l}$\R^n \times \R^{k-n}$\end{tabular}}}}% 61 | \put(0,0){\includegraphics[width=\unitlength,page=3]{submersion-theorem.pdf}}% 62 | \put(0.52130787,0.31941264){\color[rgb]{0,0,0}\makebox(0,0)[lt]{\lineheight{1.25}\smash{\begin{tabular}[t]{l}$\tau$\end{tabular}}}}% 63 | \put(0,0){\includegraphics[width=\unitlength,page=4]{submersion-theorem.pdf}}% 64 | \put(0.60156525,0.07042705){\color[rgb]{0,0,0}\makebox(0,0)[lt]{\lineheight{1.25}\smash{\begin{tabular}[t]{l}$\pi$\end{tabular}}}}% 65 | \put(0,0){\includegraphics[width=\unitlength,page=5]{submersion-theorem.pdf}}% 66 | \end{picture}% 67 | \endgroup% 68 | 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\includegraphics[width=]{.pdf} 14 | %% 15 | %% Images with a different path to the parent latex file can 16 | %% be accessed with the `import' package (which may need to be 17 | %% installed) using 18 | %% \usepackage{import} 19 | %% in the preamble, and then including the image with 20 | %% \import{}{.pdf_tex} 21 | %% Alternatively, one can specify 22 | %% \graphicspath{{/}} 23 | %% 24 | %% For more information, please see info/svg-inkscape on CTAN: 25 | %% http://tug.ctan.org/tex-archive/info/svg-inkscape 26 | %% 27 | \begingroup% 28 | \makeatletter% 29 | \providecommand\color[2][]{% 30 | \errmessage{(Inkscape) Color is used for the text in Inkscape, but the package 'color.sty' is not loaded}% 31 | \renewcommand\color[2][]{}% 32 | }% 33 | \providecommand\transparent[1]{% 34 | \errmessage{(Inkscape) Transparency is used (non-zero) for the text in Inkscape, but the package 'transparent.sty' is not loaded}% 35 | \renewcommand\transparent[1]{}% 36 | }% 37 | \providecommand\rotatebox[2]{#2}% 38 | \newcommand*\fsize{\dimexpr\f@size pt\relax}% 39 | \newcommand*\lineheight[1]{\fontsize{\fsize}{#1\fsize}\selectfont}% 40 | \ifx\svgwidth\undefined% 41 | \setlength{\unitlength}{462.32493003bp}% 42 | \ifx\svgscale\undefined% 43 | \relax% 44 | \else% 45 | \setlength{\unitlength}{\unitlength * \real{\svgscale}}% 46 | \fi% 47 | \else% 48 | \setlength{\unitlength}{\svgwidth}% 49 | \fi% 50 | \global\let\svgwidth\undefined% 51 | \global\let\svgscale\undefined% 52 | \makeatother% 53 | \begin{picture}(1,0.62490738)% 54 | \lineheight{1}% 55 | \setlength\tabcolsep{0pt}% 56 | \put(0,0){\includegraphics[width=\unitlength,page=1]{vector-bundle-definition.pdf}}% 57 | \put(0.52357417,0.12323921){\color[rgb]{0,0,0}\makebox(0,0)[lt]{\lineheight{1.25}\smash{\begin{tabular}[t]{l}$\pi$\end{tabular}}}}% 58 | \put(0.69507266,0.4022744){\color[rgb]{0,0,0}\makebox(0,0)[lt]{\lineheight{1.25}\smash{\begin{tabular}[t]{l}$E$\end{tabular}}}}% 59 | \put(0.69693592,0.0576982){\color[rgb]{0,0,0}\makebox(0,0)[lt]{\lineheight{1.25}\smash{\begin{tabular}[t]{l}$B$\end{tabular}}}}% 60 | \put(0,0){\includegraphics[width=\unitlength,page=2]{vector-bundle-definition.pdf}}% 61 | \put(-0.03412279,0.38975914){\color[rgb]{0,0,0}\makebox(0,0)[lt]{\lineheight{1.25}\smash{\begin{tabular}[t]{l}image of the zero section\end{tabular}}}}% 62 | \put(0.29664226,0.38993044){\color[rgb]{0,0,0}\makebox(0,0)[lt]{\lineheight{1.25}\smash{\begin{tabular}[t]{l}$B$\end{tabular}}}}% 63 | \end{picture}% 64 | \endgroup% 65 | -------------------------------------------------------------------------------- /differential-geometry/master.tex: -------------------------------------------------------------------------------- 1 | \documentclass[a4paper]{report} 2 | \input{preamble.tex} 3 | \DeclareMathOperator{\supp}{supp} 4 | \DeclareMathOperator{\spann}{span} 5 | \DeclareMathOperator{\Id}{Id} 6 | \DeclareMathOperator{\Ker}{Ker} 7 | \DeclareMathOperator{\im}{Im} 8 | \DeclareMathOperator{\GL}{GL} 9 | \DeclareMathOperator{\SL}{SL} 10 | \DeclareMathOperator{\Mat}{Mat} 11 | \title{Differential Geometry} 12 | \author{} 13 | \date{Based on lectures by Marco Zambon in 2019--20\\ Notes taken by Gilles Castel, proofread by Marco Zambon} 14 | \begin{document} 15 | \maketitle 16 | \tableofcontents 17 | % start lessons 18 | \input{les_01.tex} 19 | \input{les_02.tex} 20 | \input{les_03.tex} 21 | \input{les_04.tex} 22 | \input{les_05.tex} 23 | \input{les_06.tex} 24 | \input{les_07.tex} 25 | \input{les_08.tex} 26 | \input{les_09.tex} 27 | \input{les_10.tex} 28 | \input{les_11.tex} 29 | \input{les_12.tex} 30 | \input{les_13.tex} 31 | % end lessons 32 | \end{document} 33 | -------------------------------------------------------------------------------- /group-theory/figures/diagram.pdf: -------------------------------------------------------------------------------- https://raw.githubusercontent.com/gillescastel/lecture-notes/929672a96abc27eaeb6fa58b1d277b3582d28532/group-theory/figures/diagram.pdf -------------------------------------------------------------------------------- /group-theory/figures/diagram.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 'diagram.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}{177.359994bp}% 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}(1,0.64546689)% 54 | \lineheight{1}% 55 | \setlength\tabcolsep{0pt}% 56 | \put(0,0){\includegraphics[width=\unitlength,page=1]{diagram.pdf}}% 57 | \end{picture}% 58 | \endgroup% 59 | -------------------------------------------------------------------------------- /group-theory/master.tex: -------------------------------------------------------------------------------- 1 | \documentclass[nocolor]{report} 2 | \input{./preamble.tex} 3 | \title{Group theory} 4 | 5 | \DeclareMathOperator{\GL}{GL} 6 | \DeclareMathOperator{\im}{Im} 7 | \DeclareMathOperator{\Ker}{Ker} 8 | \DeclareMathOperator{\Hom}{Hom} 9 | \DeclareMathOperator{\Tr}{Tr} 10 | \DeclareMathOperator{\Hol}{Hol} 11 | \DeclareMathOperator{\Aut}{Aut} 12 | \DeclareMathOperator{\Fit}{Fitt} 13 | \DeclareMathOperator{\coker}{coker} 14 | \DeclareMathOperator{\Ext}{Ext} 15 | \DeclareMathOperator{\Tor}{Tor} 16 | \DeclareMathOperator{\Der}{Der} 17 | \DeclareMathOperator{\PDer}{PDer} 18 | \begin{document} 19 | \maketitle 20 | \tableofcontents 21 | % start lessons 22 | \input{les_01.tex} 23 | \input{les_02.tex} 24 | \input{les_03.tex} 25 | \input{les_04.tex} 26 | \input{les_05.tex} 27 | \input{les_06.tex} 28 | \input{les_07.tex} 29 | \input{les_08.tex} 30 | \input{les_09.tex} 31 | \input{les_10.tex} 32 | \input{les_11.tex} 33 | \input{les_12.tex} 34 | \input{les_13.tex} 35 | \input{les_14.tex} 36 | \input{les_15.tex} 37 | \input{les_16.tex} 38 | \input{les_17.tex} 39 | \input{les_18.tex} 40 | \input{les_19.tex} 41 | \input{les_20.tex} 42 | \input{les_21.tex} 43 | \input{les_22.tex} 44 | % end lessons 45 | \end{document} 46 | --------------------------------------------------------------------------------