On the Betti number of the union of two generic map images

Carlos Biasi, Alice K.M. Libardi, Osamu Saeki

Research output: Contribution to journalArticle

Abstract

Let f : M → N and g : K → N be generic differentiable maps of compact manifolds without boundary into a manifold such that their intersection satisfies a certain transversality condition. We show, under a certain cohomological condition, that if the images f(M) and g(K) intersect, then the (ν + 1)th Betti number of their union is strictly greater than the sum of their (ν + 1)th Betti numbers, where ν = dim M + dim K - dim N. This result is applied to the study of coincidence sets and fixed point sets.

Original languageEnglish
Pages (from-to)31-46
Number of pages16
JournalTopology and its Applications
Volume95
Issue number1
DOIs
Publication statusPublished - 1999

All Science Journal Classification (ASJC) codes

  • Geometry and Topology

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