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)"> + + + + + image/svg+xml + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + 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