Talk:Normal bordism - definitions (Ex)
(Difference between revisions)
Line 17: | Line 17: | ||
\right\} | \right\} | ||
$$ | $$ | ||
+ | where we identify $(\xi_0,M_0,i_0,f_0,\overline{f_0})\sim(\xi_1,M_1,i_1,f_1,\overline{f_1})$ iff | ||
+ | |||
+ | 1) there exists $W$ compact manifold of dimension $n+1$ such that $\partial W=\partial_0W\amalg\partial_1W$ | ||
+ | |||
+ | 2) there exists an embedding $I$: $W\to\mathbb{R}^{n+k}\times[0,1]$ such that for $j=0,1$ we have | ||
+ | $I^{-1}(\mathbb{R}^{n+k}\times\{j\})=\partial_jW$ and $W$ meets $\mathbb{R}^{n+k}\times\{j\}$ transversally | ||
</wikitex> | </wikitex> |
Revision as of 10:47, 2 April 2012
Part 1
Let be a connected finite Poincare complex of dimension and let . We define
where we identify iff
1) there exists compact manifold of dimension such that
2) there exists an embedding : such that for we have and meets transversally