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