My M2 Memoire on mapping class groups & their representations
Clarified a sentence
Replaced the expression "generalized TQTF" because apparently it refers to higher-categorical functors
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,