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2 |
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} |
5 |
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.} |
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7 |
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8 \nn{should maybe mention alternate def of blob complex (sort-of-simplicial space instead of |
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9 sort-of-simplicial set) where this action would be easy} |
7 |
10 |
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 $CH_*(X) \deq CH_*(X, X)$. |