memoire-m2

My M2 Memoire on mapping class groups & their representations

git clone: git://git.pablopie.xyz/memoire-m2
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Commit: 99da24447e4164bd6870f0afad5231683650412c
Parent: 499b2b0f13479a61016a1fffde219fbbd7bc4bf2
Author: Pablo <pablo-pie@riseup.net>
Date: Wed, 12 Jun 2024 20:27:28 +0000

Removed an unnecessary equation

Removed an equation from the statement of Birman-Hilden which was never used afterwards

Diffstat

1 file changed, 3 insertions, 5 deletions

Status	File Name	N° Changes	Insertions	Deletions
Modified	sections/presentation.tex	8	3	5

diff --git a/sections/presentation.tex b/sections/presentation.tex
@@ -309,12 +309,10 @@ not isotopic \emph{through symmetric homeomorphisms}. Birman-Hilden
 \begin{theorem}[Birman-Hilden]
   If \(\phi, \psi \in \SHomeo^+(S_\ell^b, \partial S_\ell^b)\) are isotopic
   then \(\phi\) and \(\psi\) are isotopic through symmetric homeomorphisms. In
-  particular, there are isomorphism
+  particular, there is an isomorphism
   \begin{align*}
-    \SMod(S_\ell^b) & \isoto \Mod(S_{0, 2\ell + b}) &
-    \SMod(S_\ell^b) & \isoto B_{2 g + b}            \\
-             [\phi] & \mapsto [\bar \phi]           &
-             [\phi] & \mapsto \operatorname{push}^{-1}([\bar \phi]).
+    \SMod(S_\ell^b) & \isoto \Mod(S_{0, 2\ell + b}) \\
+             [\phi] & \mapsto [\bar \phi].
   \end{align*}
 \end{theorem}