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Presentation: Added basics for images and some more text

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Joshua Moerman 12 years ago
parent
9815c145c5
commit
475deda526
6 changed files with 1682 additions and 11 deletions
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  1. 618
      images/simplex_in_X.svg
  2. 1002
      images/singular_chaincomplex.svg
  3. 6
      make
  4. 34
      presentation/presentation.tex
  5. 29
      presentation/symbols.tex
  6. 4
      thesis/preamble.tex

618
images/simplex_in_X.svg
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images/singular_chaincomplex.svg
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6
make
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@ -9,6 +9,12 @@ Presentation) pdflatex "../presentation/presentation.tex" || exit 1
pdflatex "../presentation/presentation.tex" || exit 1
mv presentation.pdf ../
;;
Symbols) pdflatex "../presentation/symbols.tex" || exit 1
pdflatex "../presentation/symbols.tex" || exit 1
scp symbols.pdf moerman@stitch.science.ru.nl:~/thesissymbols.pdf
ssh moerman@stitch.science.ru.nl 'pdf2svg thesissymbols.pdf thesissymbols.svg'
scp moerman@stitch.science.ru.nl:~/thesissymbols.svg ../
;;
Thesis) pdflatex "../thesis/DoldKan.tex" || exit 1
pdflatex "../thesis/DoldKan.tex" || exit 1
mv DoldKan.pdf ../

34
presentation/presentation.tex
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@ -28,40 +28,52 @@
\frametitle{Wat is $\Ch{\cat{Ab}}$?}
\begin{definition}
Een \emph{ketencomplex} $C$ bestaat uit abelse groepen met groepshomomorfisme:
$$ \cdots \to C_4 \to^{\del_3} C_3 \to^{\del_2} C_2 \to^{\del_1} C_1 \to^{\del_0} C_0 $$
$$ \cdots \to C_4 \tot{\del_3} C_3 \tot{\del_2} C_2 \tot{\del_1} C_1 \tot{\del_0} C_0 $$
zodat $\del_n \circ \del_{n+1} = 0$ voor alle $n \geq 1$.
zodat $\del_n \circ \del_{n+1} = 0$ voor alle $n \in \N$.
\end{definition}
\end{frame}
\begin{frame}
\frametitle{Voorbeeld}
Bekijk $\Delta^n \to X$, dwz...
Bekijk $\Delta^n \tot{f} X$, dwz... \raisebox{-.2\height}{\includegraphics{simplex_in_X}}
\bigskip
\Large $\cdots \tot{\del_2} \{\} \tot{\del_1} \{\} \tot{\del_0} \{\}$
\end{frame}
\begin{frame}
\frametitle{Is $\Ch{\cat{Ab}}$ interessant?}
Gegeven een ketencomplex $C$:
$$ \cdots \to C_4 \to^{\del_3} C_3 \to^{\del_2} C_2 \to^{\del_1} C_1 \to^{\del_0} C_0 $$
$$ \cdots \to C_4 \tot{\del_3} C_3 \tot{\del_2} C_2 \tot{\del_1} C_1 \tot{\del_0} C_0 $$
met $\del_n \circ \del_{n+1} = 0$
\bigskip
Dan geldt $im(\del_{n+1}) \trianglelefteq ker(\del_n)$
Definieer: $H_n(C) = ker(\del_n) / im(\del_{n+1})$
(met $ker(\del_0) = C_0$ per conventie)
\end{frame}
\begin{frame}
\frametitle{Voorbeeld}
$ \cdots \to C_1 \to^{\del_0} C_0 $, wat is $H_1 = ker(\del_0) / im(\del_1)$?
\begin{enumerate}
\item Triviaal
\item Niet triviaal
\end{enumerate}
$ \cdots \to C_1 \tot{\del_0} C_0 $, wat is $ H_1 = \frac{ker(\del_0)}{im(\del_1)} $?
\begin{itemize}
\item $ \sigma_1 + \sigma_2 + \sigma_3 \in ker (\del_0) $ \\
\visible<2->{
$ \del_1(\tau) = \sigma_1 + \sigma_2 + \sigma_3 $ \\
Dus $ \sigma_1 + \sigma_2 + \sigma_3 \in im (\del_1) $ \\
Dus $ 0 = [\sigma_1 + \sigma_2 + \sigma_3] \in H_1 $}
\item \visible<3->{
$ \sigma_1 + \sigma_2 + \sigma_3 \in ker (\del_0) $ \\
Maar $ \sigma_1 + \sigma_2 + \sigma_3 \not \in im (\del_1) $ \\
Dus $ 0 \neq [\sigma_1 + \sigma_2 + \sigma_3] \in H_1 $}
\end{itemize}
\end{frame}
@ -72,7 +84,7 @@
verder:
{\Large $$ H_n(N(X)) \iso \pi_n(X) $$}
waarbij $N : \cat{sAb} \to \Ch{\cat{Ab}}$.
waarbij $N : \cat{sAb} \tot{\simeq} \Ch{\cat{Ab}}$.
\end{center}
\end{frame}

29
presentation/symbols.tex
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@ -0,0 +1,29 @@
\documentclass[14pt]{beamer}
% beamer definieert 'definition' al, maar dan engels :(
% fix van:
% http://tex.stackexchange.com/questions/38392/how-to-rename-theorem-or-lemma-in-beamer-to-another-language
\usepackage[dutch]{babel}
\uselanguage{dutch}
\languagepath{dutch}
\deftranslation[to=dutch]{Definition}{Definitie}
\input{../thesis/preamble}
\begin{document}
\begin{frame}
% Symbols used in drawings
Bekijk $\Delta^n \tot{f} X$, dwz...
\Large $\cdots \tot{\del_2} \{\} \tot{\del_1} \{\} \tot{\del_0} \{\}$
$ \sigma_1 + \sigma_2 + \sigma_3 = \del(\tau) $
$ \mapsto $
$ X \subseteq \mathbb{R}^2 $
\end{frame}
\end{document}

4
thesis/preamble.tex
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@ -11,12 +11,16 @@
\newcommand{\Ch}[1]{\mathbf{Ch}(#1)}
\newcommand{\iso}{\cong}
\newcommand{\tot}[1]{\xrightarrow{\,\,{#1}\,\,}}
\newcommand{\eps}{\varepsilon}
\newcommand{\I}{\,\mid\,}
\newcommand{\then}{\Rightarrow}
\newcommand{\inject}{\hookrightarrow}
\newcommand{\del}{\partial}
% relative to the one who includes us :(
\graphicspath{ {../images/} }
\newcommand{\todo}[1]{
\addcontentsline{tdo}{todo}{\protect{#1}}
$\ast$ \marginpar{\tiny $\ast$ #1}