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ArticleOriginal scientific text

Title

A Lefschetz-type coincidence theorem

Authors 1

Affiliations

  1. Department of Mathematics, University of Illinois at Urbana-Champaign, 1409 West Green Street, Urbana, IL 61801, U.S.A.

Abstract

A Lefschetz-type coincidence theorem for two maps f,g: X → Y from an arbitrary topological space to a manifold is given: Ifg=λfg, that is, the coincidence index is equal to the Lefschetz number. It follows that if λfg≠0 then there is an x ∈ X such that f(x) = g(x). In particular, the theorem contains well-known coincidence results for (i) X,Y manifolds, f boundary-preserving, and (ii) Y Euclidean, f with acyclic fibres. It also implies certain fixed point results for multivalued maps with "point-like" (acyclic) and "sphere-like" values.

Keywords

ENG
Lefschetz coincidence theory, Lefschetz number, coincidence index, fixed point, multivalued map

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Fundamenta Mathematicae
1999/162/1
Export to PBN, Opens in new tab
Pages:
65-89
Main language of publication
English
Received
1998-07-15
Published
1999
Exact and natural sciences