My M2 Memoire on mapping class groups & their representations
Removed an unnecessary equation
Removed an equation from the statement of Birman-Hilden which was never used afterwards
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}