diff --git a/images/singular_chaincomplex.svg b/images/singular_chaincomplex.svg
index 3f09551..2e0f645 100644
--- a/images/singular_chaincomplex.svg
+++ b/images/singular_chaincomplex.svg
@@ -23,7 +23,7 @@
image/svg+xml
-
+
@@ -948,7 +948,7 @@
inkscape:groupmode="layer"
id="layer1"
inkscape:label="Slide+1"
- style="display:inline"
+ style="display:none"
transform="translate(-29.327251,-82.926998)">
+
diff --git a/images/singular_homology1.pdf b/images/singular_homology1.pdf
new file mode 100644
index 0000000..5de466f
Binary files /dev/null and b/images/singular_homology1.pdf differ
diff --git a/images/singular_homology2.pdf b/images/singular_homology2.pdf
new file mode 100644
index 0000000..76952e2
Binary files /dev/null and b/images/singular_homology2.pdf differ
diff --git a/images/singular_homology3.pdf b/images/singular_homology3.pdf
new file mode 100644
index 0000000..bb537e7
Binary files /dev/null and b/images/singular_homology3.pdf differ
diff --git a/presentation/presentation.tex b/presentation/presentation.tex
index e81d276..49c34be 100644
--- a/presentation/presentation.tex
+++ b/presentation/presentation.tex
@@ -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{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 $ \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}
+ }
- \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}
diff --git a/presentation/symbols.tex b/presentation/symbols.tex
index 957138c..5bde99e 100644
--- a/presentation/symbols.tex
+++ b/presentation/symbols.tex
@@ -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