71 %% \newcommand definitions are recommended; \def definitions are supported |
71 %% \newcommand definitions are recommended; \def definitions are supported |
72 |
72 |
73 %\newcommand{\mfrac}[2]{\frac{\displaystyle #1}{\displaystyle #2}} |
73 %\newcommand{\mfrac}[2]{\frac{\displaystyle #1}{\displaystyle #2}} |
74 %\def\s{\sigma} |
74 %\def\s{\sigma} |
75 |
75 |
76 \input{preamble} |
76 \def\bc{{\mathcal B}} |
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77 \def\btc{{\mathcal{BT}}} |
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78 |
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79 \newcommand{\HC}{\operatorname{Hoch}} |
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80 \newcommand{\HH}{\operatorname{HH}} |
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81 |
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82 \newcommand{\CM}[2]{C_*(\Maps(#1 \to #2))} |
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83 \newcommand{\CD}[1]{C_*(\Diff(#1))} |
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84 \newcommand{\CH}[1]{CH_*(#1)} |
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85 |
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86 \newcommand{\cl}[1]{\underrightarrow{#1}} |
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87 \newcommand{\clh}[1]{\underrightarrow{#1}_{{}_{{}_{{}_h}}}} |
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88 |
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89 |
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90 \newcommand{\Set}{\text{\textbf{Set}}} |
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91 \newcommand{\Vect}{\text{\textbf{Vect}}} |
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92 \newcommand{\Kom}{\text{\textbf{Kom}}} |
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93 \newcommand{\Cat}{\mathcal{C}} |
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94 |
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95 \newcommand{\cell}{\mathfrak{D}} |
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96 |
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97 \newcommand{\into}{\hookrightarrow} |
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98 \newcommand{\onto}{\twoheadrightarrow} |
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99 \newcommand{\iso}{\cong} |
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100 \newcommand{\quism}{\underset{\text{q.i.}}{\simeq}} |
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101 \newcommand{\htpy}{\simeq} |
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102 \newcommand{\actsOn}{\circlearrowright} |
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103 \newcommand{\xto}[1]{\xrightarrow{#1}} |
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104 \newcommand{\isoto}{\xto{\iso}} |
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105 \newcommand{\quismto}{\xrightarrow[\text{q.i.}]{\iso}} |
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106 \newcommand{\diffeoto}{\xrightarrow[\text{diffeo}]{\iso}} |
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107 \newcommand{\htpyto}{\xrightarrow[\text{htpy}]{\htpy}} |
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108 |
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109 \newcommand{\directSum}{\oplus} |
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110 \newcommand{\DirectSum}{\bigoplus} |
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111 \newcommand{\tensor}{\otimes} |
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112 \newcommand{\Tensor}{\bigotimes} |
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113 |
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114 \newcommand{\Bord}{\operatorname{Bord}} |
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115 |
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116 \newcommand{\selfarrow}{\ensuremath{\smash{\tikz[baseline]{\clip (0,0.36) rectangle (0.39,-0.16); \draw[->] (0,0.2) .. controls (0.5,0.6) and (0.5,-0.4) .. (0,0);}}}} |
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117 |
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118 \newcommand{\bdy}{\partial} |
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119 \newcommand{\compose}{\circ} |
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120 \newcommand{\eset}{\emptyset} |
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121 |
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122 \newcommand{\id}{\boldsymbol{1}} |
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123 |
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124 % kw_macros |
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125 |
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126 %!TEX root = ../blob1.tex |
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127 |
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128 %%%%% excerpts from KW's include file of standard macros |
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129 %%% (with various new ones added) |
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130 |
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131 \def\z{\mathbb{Z}} |
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132 \def\r{\mathbb{R}} |
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133 \def\c{\mathbb{C}} |
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134 \def\t{\mathbb{T}} |
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135 \def\ebb{\mathbb{E}} |
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136 |
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137 \def\k{{\bf k}} |
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138 |
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139 \def\du{\sqcup} |
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140 \def\bd{\partial} |
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141 \def\sub{\subset} |
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142 \def\subeq{\subseteq} |
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143 \def\sup{\supset} |
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144 %\def\setmin{\smallsetminus} |
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145 \def\setmin{\setminus} |
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146 \def\ep{\epsilon} |
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147 \def\sgl{_\mathrm{gl}} |
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148 \def\op{^\mathrm{op}} |
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149 \def\deq{\stackrel{\mathrm{def}}{=}} |
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150 \def\pd#1#2{\frac{\partial #1}{\partial #2}} |
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151 %\def\lf{\overline{\cC}} |
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152 \def\lf{\cC} |
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153 \def\ot{\otimes} |
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154 \def\vphi{\varphi} |
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155 \def\inv{^{-1}} |
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156 \def\ol{\overline} |
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157 \def\BD{BD} |
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158 |
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159 \def\spl{_\pitchfork} |
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160 |
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161 |
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162 % equations |
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163 \newcommand{\eq}[1]{\begin{displaymath}#1\end{displaymath}} |
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164 \newcommand{\eqar}[1]{\begin{eqnarray*}#1\end{eqnarray*}} |
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165 \newcommand{\eqspl}[1]{\begin{displaymath}\begin{split}#1\end{split}\end{displaymath}} |
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166 |
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167 \DeclareMathOperator*{\colim}{colim} |
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168 \DeclareMathOperator*{\hocolim}{hocolim} |
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169 |
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170 \DeclareMathOperator{\most}{most} |
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171 \DeclareMathOperator{\rest}{rest} |
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172 |
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173 |
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174 \DeclareMathOperator{\kone}{cone} |
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175 |
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176 |
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177 % new theorems |
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178 |
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179 \newtheorem{prop}{Proposition} |
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180 \newtheorem{property}[prop]{Property} |
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181 \newtheorem{thm}[prop]{Theorem} |
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182 \newtheorem{lem}[prop]{Lemma} |
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183 \newtheorem{defn}[prop]{Definition} |
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184 \newtheorem{axiom}[prop]{Axiom} |
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185 |
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186 \newenvironment{rem}{\noindent\textsl{Remark.}}{} |
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187 |
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188 % \mathrlap -- a horizontal \smash-------------------------------- |
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189 % For comparison, the existing overlap macros: |
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190 % \def\llap#1{\hbox to 0pt{\hss#1}} |
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191 % \def\rlap#1{\hbox to 0pt{#1\hss}} |
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192 \def\clap#1{\hbox to 0pt{\hss#1\hss}} |
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193 \def\mathllap{\mathpalette\mathllapinternal} |
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194 \def\mathrlap{\mathpalette\mathrlapinternal} |
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195 \def\mathclap{\mathpalette\mathclapinternal} |
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196 \def\mathllapinternal#1#2{% |
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197 \llap{$\mathsurround=0pt#1{#2}$}} |
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198 \def\mathrlapinternal#1#2{% |
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199 \rlap{$\mathsurround=0pt#1{#2}$}} |
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200 \def\mathclapinternal#1#2{% |
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201 \clap{$\mathsurround=0pt#1{#2}$}} |
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202 |
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203 % tricky way to iterate macros over a list |
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204 \def\semicolon{;} |
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205 \def\applytolist#1{ |
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206 \expandafter\def\csname multi#1\endcsname##1{ |
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207 \def\multiack{##1}\ifx\multiack\semicolon |
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208 \def\next{\relax} |
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209 \else |
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210 \csname #1\endcsname{##1} |
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211 \def\next{\csname multi#1\endcsname} |
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212 \fi |
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213 \next} |
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214 \csname multi#1\endcsname} |
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215 |
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216 % \def\cA{{\cal A}} for A..Z |
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217 \def\calc#1{\expandafter\def\csname c#1\endcsname{{\mathcal #1}}} |
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218 \applytolist{calc}QWERTYUIOPLKJHGFDSAZXCVBNM; |
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219 |
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220 % \def\bbA{{\mathbb A}} for A..Z |
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221 \def\bbc#1{\expandafter\def\csname bb#1\endcsname{{\mathbb #1}}} |
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222 \applytolist{bbc}QWERTYUIOPLKJHGFDSAZXCVBNM; |
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223 |
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224 % \def\bA{{\mathbf A}} for A..Z |
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225 \def\bfc#1{\expandafter\def\csname bf#1\endcsname{{\mathbf #1}}} |
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226 \applytolist{bfc}QWERTYUIOPLKJHGFDSAZXCVBNM; |
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227 |
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228 % \DeclareMathOperator{\pr}{pr} etc. |
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229 \def\declaremathop#1{\expandafter\DeclareMathOperator\csname #1\endcsname{#1}} |
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230 \applytolist{declaremathop}{im}{gl}{ev}{coinv}{tr}{rot}{Eq}{obj}{mor}{ob}{Rep}{Tet}{cat}{Maps}{Diff}{Homeo}{sign}{supp}{Nbd}{res}{rad}{Compat}; |
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231 |
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232 % \todo, \nn and \noop |
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233 \newcommand{\todo}[1]{\textbf{\color[rgb]{.8,.2,.5}\small TODO: #1}} |
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234 \def\nn#1{{{\color[rgb]{.2,.5,.6} \small [[#1]]}}} |
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235 \long\def\noop#1{} |
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236 |
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237 |
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238 |
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239 % references |
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240 |
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241 \newcommand{\arxiv}[1]{\href{http://arxiv.org/abs/#1}{\tt arXiv:\nolinkurl{#1}}} |
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242 \newcommand{\doi}[1]{\href{http://dx.doi.org/#1}{{\tt DOI:#1}}} |
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243 \newcommand{\euclid}[1]{\href{http://projecteuclid.org/euclid.cmp/#1}{{\tt at Project Euclid: #1}}} |
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244 \newcommand{\mathscinet}[1]{\href{http://www.ams.org/mathscinet-getitem?mr=#1}{\tt #1}} |
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245 \newcommand{\googlebooks}[1]{(preview at \href{http://books.google.com/books?id=#1}{google books})} |
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246 |
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247 |
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248 |
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249 % figures |
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250 |
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251 \newcommand{\mathfig}[2]{\ensuremath{\hspace{-3pt}\begin{array}{c}% |
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252 \raisebox{-2.5pt}{\includegraphics[width=#1\textwidth]{diagrams/#2}}% |
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253 \end{array}\hspace{-3pt}}} |
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254 |
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255 |
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256 % packages |
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257 |
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258 \usepackage{tikz} |
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259 \usetikzlibrary{shapes} |
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260 \usetikzlibrary{backgrounds} |
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261 \usetikzlibrary{decorations,decorations.pathreplacing} |
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262 \usetikzlibrary{fit,calc,through} |
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263 |
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264 \usepackage[all,color]{xy} |
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265 \SelectTips{cm}{} |
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266 |
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267 \usepackage[pdftex,plainpages=false,hypertexnames=false,pdfpagelabels]{hyperref} |
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268 |
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269 \usepackage{xcolor} |
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270 \definecolor{dark-red}{rgb}{0.7,0.25,0.25} |
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271 \definecolor{dark-blue}{rgb}{0.15,0.15,0.55} |
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272 \definecolor{medium-blue}{rgb}{0,0,0.65} |
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273 |
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274 \hypersetup{ |
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275 colorlinks, linkcolor={dark-red}, |
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276 citecolor={dark-blue}, urlcolor={medium-blue} |
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277 } |
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278 |
77 |
279 |
78 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%% |
280 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%% |
79 %% Don't type in anything in the following section: |
281 %% Don't type in anything in the following section: |
80 %%%%%%%%%%%% |
282 %%%%%%%%%%%% |
81 %% For PNAS Only: |
283 %% For PNAS Only: |