memoire-m2

My M2 Memoire on mapping class groups & their representations

preamble.tex (2773B)

 1 \usepackage{mathtools, adjustbox}
 2 \usepackage{xfrac, cancel, multicol, tabularx, relsize}
 3 \usepackage[normalem]{ulem}
 4 \usepackage[backend=biber, bibstyle=ieee]{biblatex}
 5 \usepackage{tikz-cd}
 6 \usepackage{graphicx, wrapfig}
 7 
 8 % Useful theorem definitions
 9 \theoremstyle{theorem}
10 \newboxedtheorem{theorem}{Theorem}
11 \newboxedtheorem{lemma}{Lemma}
12 \newboxedtheorem{corollary}{Corollary}
13 \newboxedtheorem{proposition}{Proposition}
14 \theoremstyle{definition}
15 \newboxedtheorem{definition}{Definition}
16 \newtheorem{example}[theorem]{Example}
17 \newtheorem{fundamental-example}[theorem]{Fundamental Example}
18 \newtheorem{observation}[theorem]{Observation}
19 \newtheorem{fundamental-observation}[theorem]{Fundamental Observation}
20 \newtheorem{fact}[theorem]{Fact}
21 \theoremstyle{remark}
22 \newtheorem*{remark}{Remark}
23 
24 % Use \blacksquare for \qed
25 \renewcommand{\qedsymbol}{\ensuremath{\blacksquare}}
26 
27 % Only use \smallsetminus
28 \renewcommand{\setminus}{\smallsetminus}
29 
30 % Make the arrow on top of \vec adjust to the content
31 \renewcommand{\vec}{\overrightarrow}
32 
33 % Get propper inequality symbols
34 \renewcommand{\leq}{\leqslant}
35 \renewcommand{\le}{\leqslant}
36 \renewcommand{\geq}{\geqslant}
37 \renewcommand{\ge}{\geqslant}
38 
39 % Fix the subset/supset symbols
40 \renewcommand{\subset}{\subseteq}
41 \renewcommand{\supset}{\supseteq}
42 
43 % A semantic alternative to \textbf
44 \newcommand{\strong}[1]{\textbf{#1}}
45 
46 % Display long arrows instead of short ones
47 \renewcommand{\to}{\longrightarrow}
48 \renewcommand{\mapsto}{\longmapsto}
49 \renewcommand{\hookrightarrow}{\lhook\joinrel\longrightarrow}
50 
51 % Isomorphism arrow
52 \newcommand{\isoto}
53   {\xlongrightarrow{\smash{\raisebox{-0.65ex}{\ensuremath{\scriptstyle\sim}}}}}
54 
55 % Fix the goddamn \chi macro!
56 % For some reason the default LaTeX fonts place this character much lower than
57 % where people actually expect it to be. This new definition place it in with
58 % the appropriate spacing
59 \renewcommand{\chi}{\ensuremath \raisebox{\depth}{$\mathchar"11F$}}
60 
61 % MCGs of a surface
62 \DeclareMathOperator{\Mod}{Mod}
63 \DeclareMathOperator{\PMod}{PMod}
64 \DeclareMathOperator{\SMod}{SMod}
65 
66 % Group of homeomorphisms
67 \DeclareMathOperator{\Homeo}{Homeo}
68 \DeclareMathOperator{\SHomeo}{SHomeo}
69 
70 % General linear group
71 \DeclareMathOperator{\GL}{GL}
72 \DeclareMathOperator{\PGL}{PGL}
73 
74 % Group Abelianization
75 \newcommand{\ab}{{\operatorname{ab}}}
76 
77 % Group action symbol
78 \newcommand{\leftaction}{\,\rotatebox[origin=c]{-90}{$\circlearrowleft$}\,}
79 \newcommand{\rightaction}{\,\rotatebox[origin=c]{90}{$\circlearrowright$}\,}
80 
81 % Quotient object
82 \newcommand{\mfrac}[2]{\mathlarger{\mathlarger{\sfrac{#1}{#2}}}}
83 
84 % A normal subobject in a pointed cathegory
85 \newcommand{\normal}{\triangleleft}
86 
87 % Useful category definitions
88 \newcommand{\Cob}{\mathbf{Cob}_3^+}
89 \newcommand{\Vect}{\mathbf{Vect}(\mathbb{C})}