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1 %auto-ignore |
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2 %this ensures the arxiv doesn't try to start TeXing here. |
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3 |
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4 \usepackage{amsmath,amssymb,amsfonts} |
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5 \usepackage{ifpdf} |
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6 |
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7 %\ifpdf |
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8 %\usepackage[pdftex,all,color]{xy} |
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9 %\else |
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10 \usepackage[all,color]{xy} |
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11 %\fi |
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12 |
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13 \SelectTips{cm}{} |
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14 % This may speed up compilation of complex documents with many xymatrices. |
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15 %\CompileMatrices |
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16 |
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17 % ---------------------------------------------------------------- |
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18 \vfuzz2pt % Don't report over-full v-boxes if over-edge is small |
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19 \hfuzz2pt % Don't report over-full h-boxes if over-edge is small |
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20 % ---------------------------------------------------------------- |
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21 |
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22 % diagrams ------------------------------------------------------- |
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23 % figures --------------------------------------------------------- |
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24 %%% borrowed from Dror's cobordisms paper, use this to include eps or pdf graphics. |
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25 \ifpdf |
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26 \newcommand{\pathtodiagrams}{\pathtotrunk diagrams/pdf/} |
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27 \else |
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28 \newcommand{\pathtodiagrams}{\pathtotrunk diagrams/eps/} |
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29 \fi |
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30 |
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31 \newcommand{\mathfig}[2]{{\hspace{-3pt}\begin{array}{c}% |
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32 \raisebox{-2.5pt}{\includegraphics[width=#1\textwidth]{\pathtodiagrams #2}}% |
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33 \end{array}\hspace{-3pt}}} |
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34 \newcommand{\reflectmathfig}[2]{{\hspace{-3pt}\begin{array}{c}% |
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35 \raisebox{-2.5pt}{\reflectbox{\includegraphics[width=#1\textwidth]{\pathtodiagrams #2}}}% |
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36 \end{array}\hspace{-3pt}}} |
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37 \newcommand{\rotatemathfig}[3]{{\hspace{-3pt}\begin{array}{c}% |
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38 \raisebox{-2.5pt}{\rotatebox{#2}{\includegraphics[height=#1\textwidth]{\pathtodiagrams #3}}}% |
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39 \end{array}\hspace{-3pt}}} |
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40 \newcommand{\placefig}[2]{\includegraphics[width=#1\linewidth]{\pathtodiagrams #2}} |
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41 |
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42 \ifpdf |
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43 \usepackage[pdftex,plainpages=false,hypertexnames=false,pdfpagelabels]{hyperref} |
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44 \else |
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45 \usepackage[dvips,plainpages=false,hypertexnames=false]{hyperref} |
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46 \fi |
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47 \newcommand{\arxiv}[1]{\href{http://arxiv.org/abs/#1}{\tt arXiv:\nolinkurl{#1}}} |
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48 \newcommand{\doi}[1]{\href{http://dx.doi.org/#1}{{\tt DOI:#1}}} |
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49 \newcommand{\mathscinet}[1]{\href{http://www.ams.org/mathscinet-getitem?mr=#1}{\tt #1}} |
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50 |
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51 |
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52 % THEOREMS ------------------------------------------------------- |
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53 \theoremstyle{plain} |
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54 \newtheorem*{fact}{Fact} |
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55 \newtheorem{prop}{Proposition}[section] |
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56 \newtheorem{conj}[prop]{Conjecture} |
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57 \newtheorem{thm}[prop]{Theorem} |
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58 \newtheorem{lem}[prop]{Lemma} |
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59 \newtheorem{lemma}[prop]{Lemma} |
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60 \newtheorem{cor}[prop]{Corollary} |
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61 \newtheorem*{cor*}{Corollary} |
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62 \newtheorem*{exc}{Exercise} |
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63 %\theoremstyle{definition} |
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64 \newtheorem{defn}[prop]{Definition} % numbered definition |
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65 \newtheorem*{defn*}{Definition} % unnumbered definition |
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66 \newtheorem{question}{Question} |
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67 \newenvironment{rem}{\noindent\textsl{Remark.}}{} % perhaps looks better than rem above? |
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68 \numberwithin{equation}{section} |
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69 %\numberwithin{figure}{section} |
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70 |
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71 % Marginal notes in draft mode ----------------------------------- |
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72 \newcommand{\scott}[1]{\stepcounter{comment}{{\color{blue} $\star^{(\arabic{comment})}$}}\marginpar{\color{blue} $\star^{(\arabic{comment})}$ \usefont{T1}{scott}{m}{n} #1 --S}} % draft mode |
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73 \newcommand{\ari}[1]{\stepcounter{comment}{\color{red} $\star^{(\arabic{comment})}$}\marginpar{\color{red} $\star^{(\arabic{comment})}$ #1 --A}} % draft mode |
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74 \newcommand{\comment}[1]{\stepcounter{comment}$\star^{(\arabic{comment})}$\marginpar{\tiny $\star^{(\arabic{comment})}$ #1}} % draft mode |
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75 \newcounter{comment} |
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76 \newcommand{\noop}[1]{} |
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77 \newcommand{\todo}[1]{\textbf{TODO: #1}} |
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78 |
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79 % \mathrlap -- a horizontal \smash-------------------------------- |
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80 % For comparison, the existing overlap macros: |
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81 % \def\llap#1{\hbox to 0pt{\hss#1}} |
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82 % \def\rlap#1{\hbox to 0pt{#1\hss}} |
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83 \def\clap#1{\hbox to 0pt{\hss#1\hss}} |
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84 \def\mathllap{\mathpalette\mathllapinternal} |
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85 \def\mathrlap{\mathpalette\mathrlapinternal} |
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86 \def\mathclap{\mathpalette\mathclapinternal} |
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87 \def\mathllapinternal#1#2{% |
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88 \llap{$\mathsurround=0pt#1{#2}$}} |
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89 \def\mathrlapinternal#1#2{% |
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90 \rlap{$\mathsurround=0pt#1{#2}$}} |
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91 \def\mathclapinternal#1#2{% |
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92 \clap{$\mathsurround=0pt#1{#2}$}} |
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93 |
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94 % MATH ----------------------------------------------------------- |
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95 \newcommand{\Natural}{\mathbb N} |
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96 \newcommand{\Integer}{\mathbb Z} |
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97 \newcommand{\Rational}{\mathbb Q} |
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98 \newcommand{\Real}{\mathbb R} |
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99 \newcommand{\Complex}{\mathbb C} |
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100 \newcommand{\Field}{\mathbb F} |
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101 |
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102 \newcommand{\Id}{\boldsymbol{1}} |
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103 \renewcommand{\imath}{\mathfrak{i}} |
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104 \renewcommand{\jmath}{\mathfrak{j}} |
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105 |
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106 \newcommand{\qRing}{\Integer[q,q^{-1}]} |
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107 \newcommand{\qMod}{\qRing-\operatorname{Mod}} |
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108 \newcommand{\ZMod}{\Integer-\operatorname{Mod}} |
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109 |
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110 \newcommand{\To}{\rightarrow} |
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111 \newcommand{\Into}{\hookrightarrow} |
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112 \newcommand{\Onto}{\mapsto} |
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113 \newcommand{\Iso}{\cong} |
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114 \newcommand{\ActsOn}{\circlearrowright} |
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115 |
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116 \newcommand{\htpy}{\simeq} |
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117 |
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118 \newcommand{\restrict}[2]{#1{}_{\mid #2}{}} |
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119 \newcommand{\set}[1]{\left\{#1\right\}} |
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120 \newcommand{\setc}[2]{\left\{#1 \;\left| \; #2 \right. \right\}} |
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121 \newcommand{\relations}[2]{\left<#1 \;\left| \; #2 \right. \right>} |
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122 \newcommand{\cone}[3]{C\left(#1 \xrightarrow{#2} #3\right)} |
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123 \newcommand{\pairing}[2]{\left\langle#1 ,#2 \right\rangle} |
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124 |
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125 \newcommand{\card}[1]{\sharp{#1}} |
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126 |
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127 \newcommand{\bdy}{\partial} |
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128 \newcommand{\compose}{\circ} |
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129 \newcommand{\eset}{\emptyset} |
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130 |
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131 \newcommand{\Cat}{\mathcal{C}} |
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132 |
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133 \newcommand{\psmallmatrix}[1]{\left(\begin{smallmatrix} #1 \end{smallmatrix}\right)} |
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134 |
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135 \newcommand{\qiq}[2]{[#1]_{#2}} |
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136 \newcommand{\qi}[1]{\qiq{#1}{q}} |
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137 \newcommand{\qdim}{\operatorname{dim_q}} |
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138 |
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139 \newcommand{\directSum}{\oplus} |
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140 \newcommand{\DirectSum}{\bigoplus} |
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141 \newcommand{\tensor}{\otimes} |
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142 \newcommand{\Tensor}{\bigotimes} |
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143 |
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144 \newcommand{\db}[1]{\left(\left(#1\right)\right)} |
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145 |
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146 \newcommand{\su}[1]{\mathfrak{su}_{#1}} |
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147 \newcommand{\csl}[1]{\mathfrak{sl}_{#1}} |
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148 \newcommand{\uqsl}[1]{U_q\left(\csl{#1}\right)} |
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149 |
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150 \newcommand{\Cobl}{{\mathcal Cob}_{/l}} |
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151 \newcommand{\Cob}[1]{{\mathcal Cob}\left(\su{#1}\right)} |
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152 \newcommand{\Kom}[1]{\operatorname{Kom}\left(#1\right)} |
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153 |
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154 \newcommand{\Mat}[1]{\mathbf{Mat}\left(#1\right)} |
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155 \newcommand{\Kar}[1]{\mathbf{Kar}\left(#1\right)} |
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156 \newcommand{\Inv}[1]{\operatorname{Inv}\left(#1\right)} |
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157 \newcommand{\Hom}[3]{\operatorname{Hom}_{#1}\left(#2,#3\right)} |
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158 \newcommand{\End}[1]{\operatorname{End}\left(#1\right)} |
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159 |
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160 \newcommand{\Gr}[2]{\text{Gr}(#1 \subset #2)} |
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161 \newcommand{\Flag}[3]{\text{Flag}(#1 \subset #2 \subset #3)} |
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162 |
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163 \def\llbracket{\left[\!\!\left[} |
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164 \def\rrbracket{\right]\!\!\right]} |
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165 \newcommand{\Kh}[1]{\llbracket#1\rrbracket} |
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166 \newcommand{\mirror}[1]{\overline{#1}}% |
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167 |
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168 \newcommand{\Tangles}{{\mathbf{Oriented Tangles}}} |
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169 \newcommand{\Spider}[1]{{\mathbf{Spider}\left(#1\right)}} |
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170 \newcommand{\TL}{\mathcal{TL}} |
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171 \newcommand{\Foam}[1]{\mathbf{Foam}\left(#1\right)} |
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172 |
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173 \newcommand{\directSumStack}[2]{{\begin{matrix}#1 \\ \DirectSum \\#2\end{matrix}}} |
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174 \newcommand{\directSumStackThree}[3]{{\begin{matrix}#1 \\ \DirectSum \\#2 \\ \DirectSum \\#3\end{matrix}}} |
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175 |
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176 \newcommand{\grading}[1]{{\color{blue}\{#1\}}} |
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177 \newcommand{\shift}[1]{\left[#1\right]} |
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178 |
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179 \newenvironment{narrow}[2]{% |
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180 \vspace{-0.4cm}% horrible hack, by scott % this only seems to be appropriate in beamer mode... |
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181 \begin{list}{}{% |
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182 \setlength{\topsep}{0pt}% |
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183 \setlength{\leftmargin}{#1}% |
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184 \setlength{\rightmargin}{#2}% |
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185 \setlength{\listparindent}{\parindent}% |
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186 \setlength{\itemindent}{\parindent}% |
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187 \setlength{\parsep}{\parskip}}% |
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188 \item[]}{\end{list}} |
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189 % ---------------------------------------------------------------- |