ISSN:
1420-8946
Keywords:
Key words. Betti number, generic map, Čech homology, Jordan-Brouwer theorem, ANR.
Source:
Springer Online Journal Archives 1860-2000
Topics:
Mathematics
Notes:
Abstract. Let $f : M \to N$ be a differentiable map of a closed m-dimensional manifold into an (m + k)-dimensional manifold with k 〉 0. We 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.
Type of Medium:
Electronic Resource
URL:
http://dx.doi.org/10.1007/PL00000368
