memoire-m2

My M2 Memoire on mapping class groups & their representations

git clone: git://git.pablopie.xyz/memoire-m2
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Commit: aff61ac3ed8fc5fd6e6ce8b8ed99937bfed7af64
Parent: 7960694cca30f591e41b5fb6d67041d37fcd4366
Author: Pablo <pablo-pie@riseup.net>
Date: Tue, 9 Jul 2024 13:06:39 +0000

Clarified a sentence

Replaced the expression "generalized TQTF" because apparently it refers to higher-categorical functors

Diffstat

1 file changed, 7 insertions, 8 deletions

Status	File Name	N° Changes	Insertions	Deletions
Modified	sections/introduction.tex	15	7	8

diff --git a/sections/introduction.tex b/sections/introduction.tex
@@ -439,14 +439,13 @@ association \(\Sigma_g \mapsto \mathcal{F}(\Sigma_g)\). Moreover, the condition
 only hold up to multiplication by scalars.
 
 Hence constructing an actual functor typically requires \emph{extending}
-\(\Cob\) and \emph{tweaking} \(\Vect\). These ``extended TQFTs'' give rise to
-linear and projective representations of the \emph{extended mapping class
-groups} \(\Mod(\Sigma_g) \times \mathbb{Z}\). We refer the reader to
-\cite{costantino, julien} for constructions of one such extended TQFT and its
-corresponding representations: the so-called \emph{\(\operatorname{SU}_2\) TQFT
-of level \(r\)}, first introduced by Witten and Reshetikhin-Tuarev
-\cite{witten, reshetikhin-turaev} in their foundational papers on quantum
-topology.
+\(\Cob\) and \emph{tweaking} \(\Vect\). Such functors give rise to linear and
+projective representations of the \emph{extended mapping class groups}
+\(\Mod(\Sigma_g) \times \mathbb{Z}\). We refer the reader to \cite{costantino,
+julien} for constructions of one such TQFT and its corresponding
+representations: the so-called \emph{\(\operatorname{SU}_2\) TQFT of level
+\(r\)}, first introduced by Witten and Reshetikhin-Tuarev \cite{witten,
+reshetikhin-turaev} in their foundational papers on quantum topology.
 
 Besides Example~\ref{ex:symplectic-rep} and Example~\ref{ex:tqft-reps}, not a
 lot of other linear representations of \(\Mod(\Sigma_g)\) are known. Indeed,