From 475deda526756f1469c9ab3d925cac10712b4d01 Mon Sep 17 00:00:00 2001 From: Joshua Moerman Date: Tue, 19 Mar 2013 12:04:23 +0100 Subject: [PATCH] Presentation: Added basics for images and some more text --- images/simplex_in_X.svg | 618 ++++++++++++++++++ images/singular_chaincomplex.svg | 1002 ++++++++++++++++++++++++++++++ make | 6 + presentation/presentation.tex | 34 +- presentation/symbols.tex | 29 + thesis/preamble.tex | 4 + 6 files changed, 1682 insertions(+), 11 deletions(-) create mode 100644 images/simplex_in_X.svg create mode 100644 images/singular_chaincomplex.svg create mode 100644 presentation/symbols.tex 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 @@ + + + + + + image/svg+xml + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + 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 @@ + + + + + + image/svg+xml + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + 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}