76 \input{preamble}

    76 \def\bc{{\mathcal B}}

    77 \def\btc{{\mathcal{BT}}}

    78 

    79 \newcommand{\HC}{\operatorname{Hoch}}

    80 \newcommand{\HH}{\operatorname{HH}}

    81 

    82 \newcommand{\CM}[2]{C_*(\Maps(#1 \to #2))}

    83 \newcommand{\CD}[1]{C_*(\Diff(#1))}

    84 \newcommand{\CH}[1]{CH_*(#1)}

    85 

    86 \newcommand{\cl}[1]{\underrightarrow{#1}}

    87 \newcommand{\clh}[1]{\underrightarrow{#1}_{{}_{{}_{{}_h}}}}

    88 

    89 

    90 \newcommand{\Set}{\text{\textbf{Set}}}

    91 \newcommand{\Vect}{\text{\textbf{Vect}}}

    92 \newcommand{\Kom}{\text{\textbf{Kom}}}

    93 \newcommand{\Cat}{\mathcal{C}}

    94 

    95 \newcommand{\cell}{\mathfrak{D}}

    96 

    97 \newcommand{\into}{\hookrightarrow}

    98 \newcommand{\onto}{\twoheadrightarrow}

    99 \newcommand{\iso}{\cong}

   100 \newcommand{\quism}{\underset{\text{q.i.}}{\simeq}}

   101 \newcommand{\htpy}{\simeq}

   102 \newcommand{\actsOn}{\circlearrowright}

   103 \newcommand{\xto}[1]{\xrightarrow{#1}}

   104 \newcommand{\isoto}{\xto{\iso}}

   105 \newcommand{\quismto}{\xrightarrow[\text{q.i.}]{\iso}}

   106 \newcommand{\diffeoto}{\xrightarrow[\text{diffeo}]{\iso}}

   107 \newcommand{\htpyto}{\xrightarrow[\text{htpy}]{\htpy}}

   108 

   109 \newcommand{\directSum}{\oplus}

   110 \newcommand{\DirectSum}{\bigoplus}

   111 \newcommand{\tensor}{\otimes}

   112 \newcommand{\Tensor}{\bigotimes}

   113 

   114 \newcommand{\Bord}{\operatorname{Bord}}

   115 

   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);}}}}

   117 

   118 \newcommand{\bdy}{\partial}

   119 \newcommand{\compose}{\circ}

   120 \newcommand{\eset}{\emptyset}

   121 

   122 \newcommand{\id}{\boldsymbol{1}}

   123 

   124 % kw_macros

   125 

   126 %!TEX root = ../blob1.tex

   127 

   128 %%%%% excerpts from KW's include file of standard macros

   129 %%% (with various new ones added)

   130 

   131 \def\z{\mathbb{Z}}

   132 \def\r{\mathbb{R}}

   133 \def\c{\mathbb{C}}

   134 \def\t{\mathbb{T}}

   135 \def\ebb{\mathbb{E}}

   136 

   137 \def\k{{\bf k}}

   138 

   139 \def\du{\sqcup}

   140 \def\bd{\partial}

   141 \def\sub{\subset}

   142 \def\subeq{\subseteq}

   143 \def\sup{\supset}

   144 %\def\setmin{\smallsetminus}

   145 \def\setmin{\setminus}

   146 \def\ep{\epsilon}

   147 \def\sgl{_\mathrm{gl}}

   148 \def\op{^\mathrm{op}}

   149 \def\deq{\stackrel{\mathrm{def}}{=}}

   150 \def\pd#1#2{\frac{\partial #1}{\partial #2}}

   151 %\def\lf{\overline{\cC}}

   152 \def\lf{\cC}

   153 \def\ot{\otimes}

   154 \def\vphi{\varphi}

   155 \def\inv{^{-1}}

   156 \def\ol{\overline}

   157 \def\BD{BD}

   158 

   159 \def\spl{_\pitchfork}

   160 

   161 

   162 % equations

   163 \newcommand{\eq}[1]{\begin{displaymath}#1\end{displaymath}}

   164 \newcommand{\eqar}[1]{\begin{eqnarray*}#1\end{eqnarray*}}

   165 \newcommand{\eqspl}[1]{\begin{displaymath}\begin{split}#1\end{split}\end{displaymath}}

   166 

   167 \DeclareMathOperator*{\colim}{colim}

   168 \DeclareMathOperator*{\hocolim}{hocolim}

   169 

   170 \DeclareMathOperator{\most}{most}

   171 \DeclareMathOperator{\rest}{rest}

   172 

   173 

   174 \DeclareMathOperator{\kone}{cone}

   175 

   176 

   177 % new theorems

   178 

   179 \newtheorem{prop}{Proposition}

   180 \newtheorem{property}[prop]{Property}

   181 \newtheorem{thm}[prop]{Theorem}

   182 \newtheorem{lem}[prop]{Lemma}

   183 \newtheorem{defn}[prop]{Definition}

   184 \newtheorem{axiom}[prop]{Axiom}

   185 

   186 \newenvironment{rem}{\noindent\textsl{Remark.}}{}

   187 

   188 % \mathrlap -- a horizontal \smash--------------------------------

   189 % For comparison, the existing overlap macros:

   190 % \def\llap#1{\hbox to 0pt{\hss#1}}

   191 % \def\rlap#1{\hbox to 0pt{#1\hss}}

   192 \def\clap#1{\hbox to 0pt{\hss#1\hss}}

   193 \def\mathllap{\mathpalette\mathllapinternal}

   194 \def\mathrlap{\mathpalette\mathrlapinternal}

   195 \def\mathclap{\mathpalette\mathclapinternal}

   196 \def\mathllapinternal#1#2{%

   197 \llap{$\mathsurround=0pt#1{#2}$}}

   198 \def\mathrlapinternal#1#2{%

   199 \rlap{$\mathsurround=0pt#1{#2}$}}

   200 \def\mathclapinternal#1#2{%

   201 \clap{$\mathsurround=0pt#1{#2}$}}

   202 

   203 % tricky way to iterate macros over a list

   204 \def\semicolon{;}

   205 \def\applytolist#1{

   206     \expandafter\def\csname multi#1\endcsname##1{

   207         \def\multiack{##1}\ifx\multiack\semicolon

   208             \def\next{\relax}

   209         \else

   210             \csname #1\endcsname{##1}

   211             \def\next{\csname multi#1\endcsname}

   212         \fi

   213         \next}

   214     \csname multi#1\endcsname}

   215 

   216 % \def\cA{{\cal A}} for A..Z

   217 \def\calc#1{\expandafter\def\csname c#1\endcsname{{\mathcal #1}}}

   218 \applytolist{calc}QWERTYUIOPLKJHGFDSAZXCVBNM;

   219 

   220 % \def\bbA{{\mathbb A}} for A..Z

   221 \def\bbc#1{\expandafter\def\csname bb#1\endcsname{{\mathbb #1}}}

   222 \applytolist{bbc}QWERTYUIOPLKJHGFDSAZXCVBNM;

   223 

   224 % \def\bA{{\mathbf A}} for A..Z

   225 \def\bfc#1{\expandafter\def\csname bf#1\endcsname{{\mathbf #1}}}

   226 \applytolist{bfc}QWERTYUIOPLKJHGFDSAZXCVBNM;

   227 

   228 % \DeclareMathOperator{\pr}{pr} etc.

   229 \def\declaremathop#1{\expandafter\DeclareMathOperator\csname #1\endcsname{#1}}

   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};

   231 

   232 % \todo, \nn and \noop

   233 \newcommand{\todo}[1]{\textbf{\color[rgb]{.8,.2,.5}\small TODO: #1}}

   234 \def\nn#1{{{\color[rgb]{.2,.5,.6} \small [[#1]]}}}

   235 \long\def\noop#1{}

   236 

   237 

   238 

   239 % references

   240 

   241 \newcommand{\arxiv}[1]{\href{http://arxiv.org/abs/#1}{\tt arXiv:\nolinkurl{#1}}}

   242 \newcommand{\doi}[1]{\href{http://dx.doi.org/#1}{{\tt DOI:#1}}}

   243 \newcommand{\euclid}[1]{\href{http://projecteuclid.org/euclid.cmp/#1}{{\tt at Project Euclid: #1}}}

   244 \newcommand{\mathscinet}[1]{\href{http://www.ams.org/mathscinet-getitem?mr=#1}{\tt #1}}

   245 \newcommand{\googlebooks}[1]{(preview at \href{http://books.google.com/books?id=#1}{google books})}

   246 

   247 

   248 

   249 % figures

   250 

   251 \newcommand{\mathfig}[2]{\ensuremath{\hspace{-3pt}\begin{array}{c}%

   252   \raisebox{-2.5pt}{\includegraphics[width=#1\textwidth]{diagrams/#2}}%

   253 \end{array}\hspace{-3pt}}}

   254 

   255 

   256 % packages

   257 

   258 \usepackage{tikz}

   259 \usetikzlibrary{shapes}

   260 \usetikzlibrary{backgrounds}

   261 \usetikzlibrary{decorations,decorations.pathreplacing}

   262 \usetikzlibrary{fit,calc,through}

   263 

   264 \usepackage[all,color]{xy}

   265 \SelectTips{cm}{}

   266 

   267 \usepackage[pdftex,plainpages=false,hypertexnames=false,pdfpagelabels]{hyperref}

   268 

   269 \usepackage{xcolor}

   270 \definecolor{dark-red}{rgb}{0.7,0.25,0.25}

   271 \definecolor{dark-blue}{rgb}{0.15,0.15,0.55}

   272 \definecolor{medium-blue}{rgb}{0,0,0.65}

   273 

   274 \hypersetup{

   275     colorlinks, linkcolor={dark-red},

   276     citecolor={dark-blue}, urlcolor={medium-blue}

   277 }

   278