Artigo
On the Betti number of the union of two generic map images
Fecha
1999-06-23Registro en:
Topology and Its Applications. Amsterdam: Elsevier B.V., v. 95, n. 1, p. 31-46, 1999.
0166-8641
10.1016/S0166-8641(97)00273-3
WOS:000080833500002
2-s2.0-15944390989
WOS000080833500002.pdf
Autor
Universidade de São Paulo (USP)
Universidade Estadual Paulista (Unesp)
Hiroshima University
Resumen
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.