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

Imagem de Miniatura




Biasi, Carlos
Libardi, Alice K. M. [UNESP]
Saeki, Osamu

Título da Revista

ISSN da Revista

Título de Volume


Elsevier B.V.


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 (upsilon + 1)th Betti number of their union is strictly greater than the sum of their (upsilon + 1)th Betti numbers, where upsilon = dim M + dim K - dim N. This result is applied to the study of coincidence sets and fixed point sets. (C) 1999 Elsevier B.V. B.V. All rights reserved.



generic map, Betti number, intersection map, coincidence set, fixed point set

Como citar

Topology and Its Applications. Amsterdam: Elsevier B.V., v. 95, n. 1, p. 31-46, 1999.