1 %auto-ignore

     2 %!TEX root = pnas.tex

     3 

     4 \def\bc{{\mathcal B}}

     5 \def\btc{{\mathcal{BT}}}

     6 

     7 \newcommand{\HC}{\operatorname{Hoch}}

     8 \newcommand{\HH}{\operatorname{HH}}

     9 

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

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

    12 \newcommand{\CH}[1]{C_*(\Homeo(#1))}

    13 

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

    15 

    16 \newcommand{\Set}{\text{\textbf{Set}}}

    17 \newcommand{\Vect}{\text{\textbf{Vect}}}

    18 \newcommand{\Kom}{\text{\textbf{Kom}}}

    19 \newcommand{\Cat}{\mathcal{C}}

    20 

    21 \newcommand{\cell}{\mathfrak{D}}

    22 

    23 \newcommand{\into}{\hookrightarrow}

    24 \newcommand{\onto}{\twoheadrightarrow}

    25 \newcommand{\iso}{\cong}

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

    27 \newcommand{\htpy}{\simeq}

    28 \newcommand{\actsOn}{\circlearrowright}

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

    30 \newcommand{\isoto}{\xto{\iso}}

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

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

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

    34 

    35 \newcommand{\directSum}{\oplus}

    36 \newcommand{\DirectSum}{\bigoplus}

    37 \newcommand{\tensor}{\otimes}

    38 \newcommand{\Tensor}{\bigotimes}

    39 

    40 \newcommand{\selfarrow}{\ensuremath{\smash{\tikz[baseline]{\draw[->] (0,0.2) .. controls (0.6,0.8) and (0.6,-0.6) .. (0,0);}}}}

    41 

    42 \newcommand{\bdy}{\partial}

    43 \newcommand{\compose}{\circ}

    44 \newcommand{\eset}{\emptyset}

    45 

    46 \newcommand{\id}{\boldsymbol{1}}

    47 

    48 \newtheorem{property}{Property}

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

    50 

    51 % \mathrlap -- a horizontal \smash--------------------------------

    52 % For comparison, the existing overlap macros:

    53 % \def\llap#1{\hbox to 0pt{\hss#1}}

    54 % \def\rlap#1{\hbox to 0pt{#1\hss}}

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

    56 \def\mathllap{\mathpalette\mathllapinternal}

    57 \def\mathrlap{\mathpalette\mathrlapinternal}

    58 \def\mathclap{\mathpalette\mathclapinternal}

    59 \def\mathllapinternal#1#2{%

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

    61 \def\mathrlapinternal#1#2{%

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

    63 \def\mathclapinternal#1#2{%

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

    65 

    66 % packages

    67 

    68 \usepackage{tikz}

    69 \usetikzlibrary{shapes}

    70 \usetikzlibrary{backgrounds}

    71 \usetikzlibrary{decorations,decorations.pathreplacing}

    72 \usetikzlibrary{fit,calc,through}

    73 

    74 \usepackage[all,color]{xy}

    75 \SelectTips{cm}{}