equal
deleted
inserted
replaced
233 C_*(P)\otimes \hom(\bc_*(M_1), \bc_*(N_1))\otimes\cdots\otimes |
233 C_*(P)\otimes \hom(\bc_*(M_1), \bc_*(N_1))\otimes\cdots\otimes |
234 \hom(\bc_*(M_{k}), \bc_*(N_{k})) \to \hom(\bc_*(M_0), \bc_*(N_0)) . |
234 \hom(\bc_*(M_{k}), \bc_*(N_{k})) \to \hom(\bc_*(M_0), \bc_*(N_0)) . |
235 \] |
235 \] |
236 It suffices to show that the above maps are compatible with the relations whereby |
236 It suffices to show that the above maps are compatible with the relations whereby |
237 $FG^n_{\overline{M}, \overline{N}}$ is constructed from the various $P$'s. |
237 $FG^n_{\overline{M}, \overline{N}}$ is constructed from the various $P$'s. |
238 This in turn follows easily from the actions of $C_*(\Homeo(\cdot\to\cdot))$ are local (compatible with gluing) and associative. |
238 This in turn follows easily from the fact that |
|
239 the actions of $C_*(\Homeo(\cdot\to\cdot))$ are local (compatible with gluing) and associative. |
239 |
240 |
240 \nn{should add some detail to above} |
241 \nn{should add some detail to above} |
241 \end{proof} |
242 \end{proof} |
242 |
243 |
243 \nn{maybe point out that even for $n=1$ there's something new here.} |
244 \nn{maybe point out that even for $n=1$ there's something new here.} |