diff --git a/images/simplex_in_X.svg b/images/simplex_in_X.svg
new file mode 100644
index 0000000..5a7bb27
--- /dev/null
+++ b/images/simplex_in_X.svg
@@ -0,0 +1,618 @@
+
+
diff --git a/images/singular_chaincomplex.svg b/images/singular_chaincomplex.svg
new file mode 100644
index 0000000..810c432
--- /dev/null
+++ b/images/singular_chaincomplex.svg
@@ -0,0 +1,1002 @@
+
+
diff --git a/make b/make
index 0ea6543..ebc08ac 100755
--- a/make
+++ b/make
@@ -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 ../
diff --git a/presentation/presentation.tex b/presentation/presentation.tex
index f1a1aa6..a0248a8 100644
--- a/presentation/presentation.tex
+++ b/presentation/presentation.tex
@@ -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}
diff --git a/presentation/symbols.tex b/presentation/symbols.tex
new file mode 100644
index 0000000..27f5424
--- /dev/null
+++ b/presentation/symbols.tex
@@ -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}
\ No newline at end of file
diff --git a/thesis/preamble.tex b/thesis/preamble.tex
index 7847cb4..62274eb 100644
--- a/thesis/preamble.tex
+++ b/thesis/preamble.tex
@@ -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}