equal
deleted
inserted
replaced
246 to show that |
246 to show that |
247 \[ |
247 \[ |
248 \bc_*(E) \simeq \cF_E(Y) . |
248 \bc_*(E) \simeq \cF_E(Y) . |
249 \] |
249 \] |
250 |
250 |
251 |
251 \nn{remark further that this still works when the map is not even a fibration?} |
252 |
252 |
253 \nn{put this later} |
253 \nn{put this later} |
254 |
254 |
255 \nn{The second approach: Choose a decomposition $Y = \cup X_i$ |
255 \nn{The second approach: Choose a decomposition $Y = \cup X_i$ |
256 such that the restriction of $E$ to $X_i$ is a product $F\times X_i$. |
256 such that the restriction of $E$ to $X_i$ is a product $F\times X_i$. |
259 And more generally to each codim-$j$ face we have an $S^{j-1}$-module. |
259 And more generally to each codim-$j$ face we have an $S^{j-1}$-module. |
260 Decorate the decomposition with these modules and do the colimit. |
260 Decorate the decomposition with these modules and do the colimit. |
261 } |
261 } |
262 |
262 |
263 \nn{There is a version of this last construction for arbitrary maps $E \to Y$ |
263 \nn{There is a version of this last construction for arbitrary maps $E \to Y$ |
264 (not necessarily a fibration).} |
264 (not necessarily a fibration). |
|
265 In fact, there is also a version of the first construction for non-fibrations.} |
265 |
266 |
266 |
267 |
267 |
268 |
268 \subsection{A gluing theorem} |
269 \subsection{A gluing theorem} |
269 \label{sec:gluing} |
270 \label{sec:gluing} |