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Adds images to the presentation

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Joshua Moerman 10 years ago
parent
1177b83309
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2143582542
15 changed files with 1648 additions and 12 deletions
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  1. 7
      presentation/Makefile
  2. 25
      presentation/Rational_Homotopy_Theory.tex
  3. BIN
      presentation/images/fundamental_group.pdf
  4. 647
      presentation/images/fundamental_group.svg
  5. BIN
      presentation/images/infinite_telescope.pdf
  6. BIN
      presentation/images/infinite_telescope.pdf-rect9055-982.png
  7. 313
      presentation/images/infinite_telescope.svg
  8. 99
      presentation/images/spheres.svg
  9. 70
      presentation/images/spheres1.pdf
  10. 70
      presentation/images/spheres2.pdf
  11. 185
      presentation/images/tube.svg
  12. 142
      presentation/images/weak_eqs.svg
  13. 72
      presentation/images/weak_eqs1.pdf
  14. BIN
      presentation/images/weak_eqs2.pdf
  15. 30
      presentation/symbols.tex

7
presentation/Makefile
View File

@ -16,5 +16,12 @@ haltfast: dirs
xelatex -file-line-error -output-directory=build --halt-on-error Rational_Homotopy_Theory.tex
cp build/Rational_Homotopy_Theory.pdf ./
symbols: dirs
xelatex -file-line-error -output-directory=build symbols.tex
xelatex -file-line-error -output-directory=build symbols.tex
scp build/symbols.pdf moerman@stitch.science.ru.nl:~/rathtpy_images.pdf
ssh moerman@stitch.science.ru.nl 'pdf2svg rathtpy_images.pdf rathtpy_images.svg'
scp moerman@stitch.science.ru.nl:~/rathtpy_images.svg ./symbols.svg
dirs:
mkdir -p build

25
presentation/Rational_Homotopy_Theory.tex
View File

@ -7,6 +7,8 @@
\usepackage{tabularx}
\renewcommand{\tabularxcolumn}[1]{p{#1}}
\graphicspath{ {../presentation/images/} }
\newcommand{\Frame}[2]{
\begin{frame}{#1}#2\end{frame}
}
@ -32,21 +34,20 @@
\section{Introduction to homotopy theory}
\Frame{Homotopy theory}{
\begin{center}
Study of space or shapes \\
Study of spaces or shapes \\
with ``weak equivalences''
\bigskip
\td{plaatje}
\includegraphics{weak_eqs2}
\end{center}
}
\Frame{Important spaces}{
\td{plaatjes}
\begin{align*}
S^1 &= ... \\[1em]
S^2 &= ... \\[1em]
S^3 &= \cdots \\[1em]
&\cdots
S^1 &= \raisebox{-0.4\height}{\includegraphics{spheres1}} \\[1em]
S^2 &= \raisebox{-0.4\height}{\includegraphics{spheres2}} \\[1em]
S^3 &= \>\> \cdots \\[1em]
&\>\> \vdots
\end{align*}
}
@ -56,7 +57,7 @@
\[ \pi_1(X) = \text{maps } S^1 \to X \text{ up to homotopy} \]
\bigskip
\td{plaatje}
\includegraphics{fundamental_group}
}
\Frame{Important tools}{
@ -66,7 +67,7 @@
\pi_1(X) &= \text{maps } S^1 \to X \text{ up to homotopy} \\[1em]
\pi_2(X) &= \text{maps } S^2 \to X \text{ up to homotopy} \\[1em]
\pi_3(X) &= \text{maps } S^3 \to X \text{ up to homotopy} \\[1em]
&\cdots
&\>\>\vdots
\end{align*}
}
@ -109,7 +110,7 @@
$X$ is \emph{rational} if $\pi_n(X)$ is a $\Q$-vector space
\bigskip
\td{plaatje telescoop}
\[ S^1_\Q = \raisebox{-0.55\height}{\includegraphics{infinite_telescope}} \]
}
@ -177,8 +178,8 @@
homotopy $$h: X \times I \to Y$$
& homotopy $$h: A \to B \tensor \Lambda(t, dt)$$ \\[1em]
$f: X \to Y$ weak equivalence if $\pi_n(f): \pi_n(X) \iso \pi_n(Y)$
& $f: A \to B$ weak equivalence if $H(f): H(X) \iso H(Y)$
weak equivalence $$\pi_n(f): \pi_n(X) \iso \pi_n(Y)$$
& weak equivalence if $$H(f): H(X) \iso H(Y)$$
}
}

BIN
presentation/images/fundamental_group.pdf
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647
presentation/images/fundamental_group.svg
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@ -0,0 +1,647 @@
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\documentclass[14pt]{beamer}
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\newcommand{\td}[1]{\colorbox{todocolor}{*\footnote{TODO: #1}}}
\input{preamble}
\usepackage{tabularx}
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\title{Rational Homotopy Theory}
\author{Joshua Moerman}
\institute[Radboud Universiteit Nijmegen]{Supervisor: Ieke Moerdijk}
\date{}
\begin{document}
\Frame{}{
\[ 1 \times \]
\[ 2 \times \]
\[ 3 \times \]
\[ 4 \times \]
}
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