memoire-m2

My M2 Memoire on mapping class groups & their representations

git clone: git://git.pablopie.xyz/memoire-m2
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Commit: 95fbf362def57dc0b4c800cc01662c44210fd63e
Parent: 2f6478d4ac35a2cb4274e8e555f4cd86ba683de1
Author: Pablo <pablo-pie@riseup.net>
Date: Sun, 23 Jun 2024 09:13:28 +0000

Added some TODO items

Diffstat

2 files changed, 3 insertions, 0 deletions

Status	File Name	N° Changes	Insertions	Deletions
Modified	sections/introduction.tex	2	2	0
Modified	sections/presentation.tex	1	1	0

diff --git a/sections/introduction.tex b/sections/introduction.tex
@@ -354,6 +354,8 @@ S_1\) and the once-punctured torus \(S_{1, 1}\).
   By the same token, \(\Mod(S_{1, 1}) \cong \operatorname{SL}_2(\mathbb{Z})\).
 \end{example}
 
+% TODO: Add comments on the proof of linearity of Mod(S_2) by Korkmaz and
+% Bigelow-Budney?
 \begin{note}
   Despite the fact \(\psi : \Mod(\mathbb{T}^2) \to
   \operatorname{SL}_2(\mathbb{Z})\) is an isomorphism, the symplectic

diff --git a/sections/presentation.tex b/sections/presentation.tex
@@ -9,6 +9,7 @@ geometry of curves in \(S_g\) -- see Theorem~\ref{thm:wajnryb-presentation}.
 
 We start by the so called \emph{lantern relation}.
 
+% TODO: Add a sketch of proof?
 \begin{fundamental-observation}
   Let \(S_0^4\) be the surface the of genus \(0\) with \(4\) boundary
   components -- i.e. the \emph{lantern-like} surface we get by subtracting