equal
deleted
inserted
replaced
19 e_{XY} : CH_*(X, Y) \otimes \bc_*(X) \to \bc_*(Y) |
19 e_{XY} : CH_*(X, Y) \otimes \bc_*(X) \to \bc_*(Y) |
20 } |
20 } |
21 such that |
21 such that |
22 \begin{enumerate} |
22 \begin{enumerate} |
23 \item on $CH_0(X, Y) \otimes \bc_*(X)$ it agrees with the obvious action of |
23 \item on $CH_0(X, Y) \otimes \bc_*(X)$ it agrees with the obvious action of |
24 $\Homeo(X, Y)$ on $\bc_*(X)$ (Proposition (\ref{diff0prop})), and |
24 $\Homeo(X, Y)$ on $\bc_*(X)$ (Property (\ref{property:functoriality})), and |
25 \item for any compatible splittings $X\to X\sgl$ and $Y\to Y\sgl$, |
25 \item for any compatible splittings $X\to X\sgl$ and $Y\to Y\sgl$, |
26 the following diagram commutes up to homotopy |
26 the following diagram commutes up to homotopy |
27 \eq{ \xymatrix{ |
27 \eq{ \xymatrix{ |
28 CH_*(X\sgl, Y\sgl) \otimes \bc_*(X\sgl) \ar[r]^(.7){e_{X\sgl Y\sgl}} \ar[d]^{\gl \otimes \gl} & \bc_*(Y\sgl) \ar[d]_{\gl} \\ |
28 CH_*(X\sgl, Y\sgl) \otimes \bc_*(X\sgl) \ar[r]^(.7){e_{X\sgl Y\sgl}} \ar[d]^{\gl \otimes \gl} & \bc_*(Y\sgl) \ar[d]_{\gl} \\ |
29 CH_*(X, Y) \otimes \bc_*(X) |
29 CH_*(X, Y) \otimes \bc_*(X) |