memoire-m2

My M2 Memoire on mapping class groups & their representations

memoir.tex (2303B)

 1 \documentclass{memoires}
 2 \input{./preamble.tex}
 3 \addbibresource{references.bib}
 4 
 5 \title{Mapping Class Groups \\ \& \\ their Representations}
 6 \author{Thiago Brevidelli Garcia}
 7 \dedication{This master thesis is dedicated to my dear friend Lucas Schiezari. \\ May he rest in peace.}
 8 
 9 \begin{document}
10 
11 \makecover
12 \maketitle
13 
14 \begin{about}
15   This is my M2 Memoir (Master Thesis), written in June 2024 under the
16   supervision of professor Maxime Wolff of the Institut of Mathématiques de
17   Toulouse (IMT), France. The subject of the dissertation at hand is the notion
18   of the mapping class group of a surface, their linear representations and
19   some recent developments in the field. Namely, we discuss Korkmaz' proof of
20   the triviality of low-dimensional representations.
21 
22   Throughout these notes we will follow some guiding principles. First, lengthy
23   proofs are favored as opposed to collections of smaller lemmas. This is a
24   deliberate effort to emphasize the relevant results. That said, this
25   dissertation is meant to be concise. Hence numerous results are left
26   unproved. We refer the reader to proofs in other materials when appropriate.
27 
28   Our main references are the beautiful book by Farb-Margalit
29   \cite{farb-margalit}, as well as the 2023 article by Korkmaz \cite{korkmaz}.
30   We assume the reader is already familiar with basic topology and group
31   theory. Crucially, we \emph{do not} assume any familiarity with
32   representation theory.
33 
34   \section*{Acknowledgments}
35 
36   I would like to thank my friends and family for their tireless love and
37   support. Special thanks to my girlfriend for her endless encouragement and
38   understanding during this challenging year. I should also thank M. Faitg for
39   his help with the discussion on TQFT representations.
40 
41   \section*{License}
42 
43   This document was typeset and compiled using free software. Its \LaTeX~source
44   code is freely available at \url{https://git.pablopie.xyz/memoire-m2}, for
45   distribution under the terms of the
46   \href{https://creativecommons.org/licenses/by/4.0/}{Creative Commons
47   Attribution 4.0 license}.
48 \end{about}
49 
50 \tableofcontents
51 
52 \input{sections/introduction}
53 
54 \input{sections/twists}
55 
56 \input{sections/presentation}
57 
58 \input{sections/representations}
59 
60 \printbibliography
61 
62 % Backcover
63 \makecover[b]
64 \end{document}
65