- Commit
- f48da189d8d8cfb546f57b29b62391d766c0a7c9
- Parent
- 54dfcca270c2f192086c2190de1ac9c14a3e317b
- Author
- Pablo <pablo-pie@riseup.net>
- Date
Added a clarification
My M2 Memoire on mapping class groups & their representations
Added a clarification
1 file changed, 6 insertions, 5 deletions
Status | File Name | N° Changes | Insertions | Deletions |
Modified | sections/representations.tex | 11 | 6 | 5 |
diff --git a/sections/representations.tex b/sections/representations.tex @@ -2,11 +2,12 @@ Having built a solid understanding of the combinatorics of Dehn twists, we are now ready to attack the problem of classifying the representations of -\(\Mod(S_g)\). Indeed, in light of the Wajnryb presentation, a representation -\(\rho : \Mod(S_g) \to \GL_n(\mathbb{C})\) is nothing other than a choice of -\(2g + 1\) matrices \(\rho(\tau_{\alpha_1}), \ldots, \rho(\tau_{\alpha_{2g}}) -\in \GL_n(\mathbb{C})\) satisfying the relations \strong{(i)} to \strong{(v)} -from Theorem~\ref{thm:wajnryb-presentation}. +sufficiently small dimension of \(\Mod(S_g)\) . Indeed, in light of the Wajnryb +presentation, a representation \(\rho : \Mod(S_g) \to \GL_n(\mathbb{C})\) is +nothing other than a choice of \(2g + 1\) matrices \(\rho(\tau_{\alpha_1}), +\ldots, \rho(\tau_{\alpha_{2g}}) \in \GL_n(\mathbb{C})\) satisfying the +relations \strong{(i)} to \strong{(v)} from +Theorem~\ref{thm:wajnryb-presentation}. Historically, these relations have been exploited by Funar \cite{funar}, Franks-Handel \cite{franks-handel} and others to establish the triviality of