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226 near $\bd V$, the expressions $p(V) \sub X$ and $p(X\setmin V) \sub X$ are |
226 near $\bd V$, the expressions $p(V) \sub X$ and $p(X\setmin V) \sub X$ are |
227 unambiguous.) |
227 unambiguous.) |
228 We have $\deg(p'') = 0$ and, inductively, $f'' = p''(b'')$. |
228 We have $\deg(p'') = 0$ and, inductively, $f'' = p''(b'')$. |
229 %We also have that $\deg(b'') = 0 = \deg(p'')$. |
229 %We also have that $\deg(b'') = 0 = \deg(p'')$. |
230 Choose $x' \in \bc_*(p(V))$ such that $\bd x' = f'$. |
230 Choose $x' \in \bc_*(p(V))$ such that $\bd x' = f'$. |
231 This is possible by \ref{bcontract}, \ref{disjunion} and the fact that isotopic fields |
231 This is possible by Properties \ref{property:disjoint-union} and \ref{property:contractibility} and the fact that isotopic fields |
232 differ by a local relation \nn{give reference?}. |
232 differ by a local relation \nn{give reference?}. |
233 Finally, define |
233 Finally, define |
234 \[ |
234 \[ |
235 e(p\ot b) \deq x' \bullet p''(b'') . |
235 e(p\ot b) \deq x' \bullet p''(b'') . |
236 \] |
236 \] |