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Presentation: Added more images, for homology slides

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Joshua Moerman 12 years ago
parent
58e9bf8fda
commit
cad8a92fb7
7 changed files with 801 additions and 27 deletions
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  1. 12
      images/singular_chaincomplex.svg
  2. 760
      images/singular_homology.svg
  3. BIN
      images/singular_homology1.pdf
  4. BIN
      images/singular_homology2.pdf
  5. BIN
      images/singular_homology3.pdf
  6. 38
      presentation/presentation.tex
  7. 16
      presentation/symbols.tex

12
images/singular_chaincomplex.svg
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@ -23,7 +23,7 @@
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presentation/presentation.tex
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@ -8,6 +8,8 @@
\languagepath{dutch}
\deftranslation[to=dutch]{Definition}{Definitie}
\usepackage{array}
\input{../thesis/preamble}
\title{Dold-Kan correspondentie
@ -49,7 +51,7 @@
\begin{frame}
\frametitle{Is $\Ch{\cat{Ab}}$ interessant?}
\frametitle{Interessant?}
Gegeven een ketencomplex $C$:
$$ \cdots \to C_4 \tot{\del_3} C_3 \tot{\del_2} C_2 \tot{\del_1} C_1 \tot{\del_0} C_0 $$
met $\del_n \circ \del_{n+1} = 0$
@ -57,7 +59,7 @@
Dan geldt $im(\del_{n+1}) \trianglelefteq ker(\del_n)$
Definieer: $H_n(C) = ker(\del_n) / im(\del_{n+1})$
Definieer: $H_n(C) = ker(\del_{n-1}) / im(\del_n)$
(met $ker(\del_0) = C_0$ per conventie)
\end{frame}
@ -66,18 +68,30 @@
\begin{frame}
\frametitle{Voorbeeld}
$ \cdots \to C_1 \tot{\del_0} C_0 $, wat is $ H_1 = \frac{ker(\del_0)}{im(\del_1)} $?
\bigskip
\begin{itemize}
\item $ \sigma_1 + \sigma_2 + \sigma_3 \in ker (\del_0) $ \\
\begin{tabular}{m{0.3\textwidth} m{0.7\textwidth}}
\includegraphics<1>{singular_homology1}
\includegraphics<2->{singular_homology2}
&
$ \sigma_1 - \sigma_2 + \sigma_3 \in ker (\del_0) $ \newline
\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}
$ \del_1(\tau) = \sigma_1 - \sigma_2 + \sigma_3 $ \newline
Dus $ \sigma_1 + \sigma_2 - \sigma_3 \in im (\del_1) $ \newline
Dus $ 0 = [\sigma_1 - \sigma_2 + \sigma_3] \in H_1 $}
\end{tabular}
\bigskip
\visible<3->{
\begin{tabular}{m{0.3\textwidth} m{0.7\textwidth}}
\includegraphics{singular_homology3}
&
$ \sigma_1 - \sigma_2 + \sigma_3 \in ker (\del_0) $ \newline
Maar $ \sigma_1 - \sigma_2 + \sigma_3 \not \in im (\del_1) $ \newline
Dus $ 0 \neq [\sigma_1 - \sigma_2 + \sigma_3] \in H_1 $
\end{tabular}
}
\end{frame}

16
presentation/symbols.tex
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@ -15,18 +15,18 @@
\begin{document}
% \begin{frame}
% % Symbols used in drawings
% Bekijk $\Delta^n \tot{f} X$, dwz...
\begin{frame}
% Symbols used in drawings
Bekijk $\Delta^n \tot{f} X$, dwz...
% \Large $\cdots \tot{\del_2} \{\} \tot{\del_1} \{\} \tot{\del_0} \{\}$
\Large $\cdots \tot{\del_2} \{\} \tot{\del_1} \{\} \tot{\del_0} \{\}$
% $ \sigma_1 + \sigma_2 + \sigma_3 = \del(\tau) $
$ \sigma_1 + \sigma_2 + \sigma_3 = \del(\tau) $
% $ \mapsto $
$ \mapsto $
% $ X \subseteq \mathbb{R}^2 $
% \end{frame}
$ X \subseteq \mathbb{R}^2 $
\end{frame}
\begin{frame}
% Symbols used in drawings