- Commit
- 42dd39d46fb24450e228ba1c2fb0f76818749f4c
- Parent
- e35c098d6902da151121e67510c3017458aad8fa
- Author
- Pablo <pablo-pie@riseup.net>
- Date
Fixed the formatting of the 2nd chapter
memoire-m2
My M2 Memoire on mapping class groups & their representations
Diffstat
1 file changed, 6 insertions, 3 deletions
| Status | File Name | N° Changes | Insertions | Deletions |
| Modified | sections/twists.tex | 9 | 6 | 3 |
diff --git a/sections/twists.tex b/sections/twists.tex @@ -454,11 +454,14 @@ Theorem~\ref{thm:mcg-is-fg}. \label{fig:torus-mcg-generators} \end{figure} + \newpage + Now suppose \(\PMod(\Sigma_{g, r})\) is finitely-generated by twists about nonseparating curves for \(g \ge 2\) or \(g = 1\) and \(r > 1\). In both - case, \(\chi(\Sigma_{g, r}) = 2 - 2g - r < 0\) and thus \(\pi_1(\Homeo^+(\Sigma_{g, - r})) = 1\) -- see \cite[Theorem~1.14]{farb-margalit}. The Birman exact - sequence from Theorem~\ref{thm:birman-exact-seq} then gives us + case, \(\chi(\Sigma_{g, r}) = 2 - 2g - r < 0\) and thus + \(\pi_1(\Homeo^+(\Sigma_{g, r})) = 1\) -- see + \cite[Theorem~1.14]{farb-margalit}. The Birman exact sequence from + Theorem~\ref{thm:birman-exact-seq} then gives us \begin{center} \begin{tikzcd} 1 \rar