- Commit
- f87f15c570cf70f02a35641091e7fd7e2f1f78e3
- Parent
- 3944f17785f55710dea6c745f8fdc27a245573d5
- Author
- Pablo <pablo-pie@riseup.net>
- Date
Fixed the formatting of double columns
Made it so that double columns are not indented
My M2 Memoire on mapping class groups & their representations
Fixed the formatting of double columns
Made it so that double columns are not indented
3 files changed, 25 insertions, 20 deletions
Status | File Name | N° Changes | Insertions | Deletions |
Modified | sections/introduction.tex | 13 | 7 | 6 |
Modified | sections/presentation.tex | 15 | 8 | 7 |
Modified | sections/twists.tex | 17 | 10 | 7 |
diff --git a/sections/introduction.tex b/sections/introduction.tex @@ -288,18 +288,19 @@ representation.} \emph{the symplectic representation of \(\Mod(\Sigma_g)\)}. \end{example} -\begin{minipage}[b]{.45\linewidth} +\noindent +\begin{minipage}[b]{.47\linewidth} \centering - \includegraphics[width=\linewidth]{images/homology-generators.eps} + \includegraphics[width=.9\linewidth]{images/homology-generators.eps} \captionof{figure}{The curves $\alpha_1, \beta_1, \ldots, \alpha_g, \beta_g \subset \Sigma_g$ that generate its first homology group.} \label{fig:homology-basis} \end{minipage} -\hspace{.5cm} % -\begin{minipage}[b]{.45\linewidth} +\hspace{.6cm} % +\begin{minipage}[b]{.47\linewidth} \centering - \includegraphics[width=\linewidth]{images/intersection-index.eps} - \vspace*{.4cm} + \includegraphics[width=.9\linewidth]{images/intersection-index.eps} + \vspace*{.75cm} \captionof{figure}{The index of an intersection point $x \in \alpha \cap \beta$.} \label{fig:intersection-index}
diff --git a/sections/presentation.tex b/sections/presentation.tex @@ -152,8 +152,8 @@ get\dots isomorphism. \end{proposition} - -\begin{minipage}[b]{.45\linewidth} +\noindent +\begin{minipage}[b]{.47\linewidth} \begin{observation}\label{ex:braid-group-center} Using the capping exact sequence from Example~\ref{ex:capping-seq} and the Alexander method, one can check that the center \(Z(\Mod(\Sigma_{0, n}^1))\) @@ -166,8 +166,8 @@ get\dots generated by \(z = (\sigma_1 \cdots \sigma_{n - 1})^n\). \end{observation} \end{minipage} -\hspace{.5cm} % -\begin{minipage}[b]{.45\textwidth} +\hspace{.6cm} % +\begin{minipage}[b]{.47\textwidth} \centering \includegraphics[width=.4\linewidth]{images/braid-group-center.eps} \captionof{figure}{The clockwise rotation by $\sfrac{2\pi}{n}$ about an axis @@ -369,7 +369,8 @@ to obtain other relations. Since \(\iota\) has \(2g + 2\) fixed points in \end{align} \end{fundamental-observation} -\begin{minipage}[b]{.45\textwidth} +\noindent +\begin{minipage}[b]{.47\textwidth} \centering \includegraphics[width=.7\linewidth]{images/hyperelliptic-relation.eps} \vspace*{.5cm} @@ -377,8 +378,8 @@ to obtain other relations. Since \(\iota\) has \(2g + 2\) fixed points in $\Mod(\Sigma_g)$ and the curve $\delta$ from the hyperelliptic relations.} \label{fig:hyperellipitic-relations} \end{minipage} -\hspace{.5cm} % -\begin{minipage}[b]{.45\textwidth} +\hspace{.6cm} % +\begin{minipage}[b]{.47\textwidth} \centering \includegraphics[width=.33\linewidth]{images/sphere-rotation.eps} \captionof{figure}{The clockwise rotation by $\sfrac{\pi}{g + 1}$ about an
diff --git a/sections/twists.tex b/sections/twists.tex @@ -60,7 +60,8 @@ applications of the Alexander method. \mathbb{Z}\). \end{example} -\begin{minipage}[b]{.45\linewidth} +\noindent +\begin{minipage}[b]{.47\linewidth} \centering \includegraphics[width=.7\linewidth]{images/dehn-twist-cylinder.eps} \captionof{figure}{The generator $f$ of $\Mod(\mathbb{S}^1 \times [0, 1]) @@ -68,8 +69,8 @@ applications of the Alexander method. the right-hand side that winds about the curve $\alpha$.} \label{fig:dehn-twist-cylinder} \end{minipage} -\hspace{.5cm} % -\begin{minipage}[b]{.45\linewidth} +\hspace{.6cm} % +\begin{minipage}[b]{.47\linewidth} \centering \includegraphics[width=.4\linewidth]{images/half-twist-disk.eps} \captionof{figure}{The generator $f$ of $\Mod(\mathbb{D}^2 \setminus @@ -528,14 +529,16 @@ remaining curves, from which we get the so called \emph{Humphreys generators}. Figure~\ref{fig:humphreys-gens}. \end{corollary} -\begin{minipage}[b]{.45\linewidth} +\noindent +\begin{minipage}[b]{.47\linewidth} \centering \includegraphics[width=\linewidth]{images/lickorish-gens.eps} - \captionof{figure}{The curves from Lickorish generators of $\Mod(\Sigma_g^p)$.} + \captionof{figure}{The curves from Lickorish generators of + $\Mod(\Sigma_g^p)$.} \label{fig:lickorish-gens} \end{minipage} -\hspace{.5cm} % -\begin{minipage}[b]{.45\textwidth} +\hspace{.6cm} % +\begin{minipage}[b]{.47\textwidth} \centering \includegraphics[width=\linewidth]{images/humphreys-gens.eps} \captionof{figure}{The curves from Humphreys generators of $\Mod(\Sigma_g)$.}