On the Betti number of the union of two generic map images
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Undergraduate course
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Elsevier B.V.
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Elsevier
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Article
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Acesso aberto
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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 (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.
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English
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Topology and Its Applications. Amsterdam: Elsevier B.V., v. 95, n. 1, p. 31-46, 1999.
