memoire-m2

My M2 Memoire on mapping class groups & their representations

memoire.tex (2499B)

 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's 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 Mémoire (Master's 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 over collections of smaller lemmas. This is a deliberate
24   effort to emphasize the relevant results. That said, this dissertation is
25   intended to be concise. Hence numerous results are left unproved. We refer
26   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. Because of tight deadlines, we have opted to
33   hand-draw all the figures.
34 
35   \section*{Acknowledgments}
36 
37   I would like to thank my friends and family for their tireless love and
38   support. Special thanks to my girlfriend for her encouragement and
39   understanding during this challenging year. I extend my gratitude to
40   Professor Wolff for accepting me as his student and providing me with his
41   invaluable guidance. I should also thank Matthieu Faitg for his help with the
42   discussion on TQFT representations.
43 
44   \section*{License}
45 
46   This document was typeset and compiled using free software. Its \LaTeX~source
47   code is freely available at \url{https://git.pablopie.xyz/memoire-m2}, for
48   distribution under the terms of the
49   \href{https://creativecommons.org/licenses/by/4.0/}{Creative Commons
50   Attribution 4.0 license}.
51 \end{about}
52 
53 \tableofcontents
54 
55 \input{sections/introduction}
56 
57 \input{sections/twists}
58 
59 \input{sections/presentation}
60 
61 \input{sections/representations}
62 
63 \printbibliography
64 
65 % Backcover
66 \makecover[b]
67 \end{document}
68