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