Abstract
Let f : M → N be a differentiable map of a closed m-dimensional manifold into an (m + k)-dimerisional manifold with k > 0. VVe show, assuming that f is generic in a certain sense, that f is an embedding if and only if the (m - k + 1)-th Betti numbers with respect to the Čech homology of M and f(M) coincide, under a certain condition on the stable normal bundle of f. This generalizes the authors' previous result for immersions with normal crossings [BS1]. As a corollary, we obtain the converse of the Jordan-Brouwer theorem for codimension-1 generic maps, which is a generalization of the results of [BR, BMS1, BMS2, Sae1] for immersions with normal crossings.
Original language | English |
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Pages (from-to) | 72-83 |
Number of pages | 12 |
Journal | Commentarii Mathematici Helvetici |
Volume | 72 |
Issue number | 1 |
DOIs | |
Publication status | Published - 1997 |
Externally published | Yes |
All Science Journal Classification (ASJC) codes
- Mathematics(all)