text/evmap.tex
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     3 \section{Action of \texorpdfstring{$\CH{X}$}{$C_*(Homeo(M))$}}
     3 \section{Action of \texorpdfstring{$\CH{X}$}{$C_*(Homeo(M))$}}
     4 \label{sec:evaluation}
     4 \label{sec:evaluation}
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     5 
     6 \nn{should comment at the start about any assumptions about smooth, PL etc.}
     6 \nn{should comment at the start about any assumptions about smooth, PL etc.}
       
     7 
       
     8 \nn{should maybe mention alternate def of blob complex (sort-of-simplicial space instead of
       
     9 sort-of-simplicial set) where this action would be easy}
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     8 Let $CH_*(X, Y)$ denote $C_*(\Homeo(X \to Y))$, the singular chain complex of
    11 Let $CH_*(X, Y)$ denote $C_*(\Homeo(X \to Y))$, the singular chain complex of
     9 the space of homeomorphisms
    12 the space of homeomorphisms
    10 between the $n$-manifolds $X$ and $Y$ (any given singular chain extends a fixed homeomorphism $\bd X \to \bd Y$).
    13 between the $n$-manifolds $X$ and $Y$ (any given singular chain extends a fixed homeomorphism $\bd X \to \bd Y$).
    11 We also will use the abbreviated notation $CH_*(X) \deq CH_*(X, X)$.
    14 We also will use the abbreviated notation $CH_*(X) \deq CH_*(X, X)$.