Geodesic
A Lefschetz-type coincidence theorem
Fundamenta Mathematicae, Tome 162 (1999) no. 1, pp. 65-89

Voir la notice de l'article provenant de la source Institute of Mathematics Polish Academy of Sciences

A Lefschetz-type coincidence theorem for two maps f,g: X → Y from an arbitrary topological space to a manifold is given: $I_{fg} = λ _{fg}$, that is, the coincidence index is equal to the Lefschetz number. It follows that if $λ_{fg} ≠ 0$ 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.
DOI : 10.4064/fm-162-1-65-89
Keywords: Lefschetz coincidence theory, Lefschetz number, coincidence index, fixed point, multivalued map

Peter Saveliev 1

1 
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Peter Saveliev. A Lefschetz-type coincidence theorem. Fundamenta Mathematicae, Tome 162 (1999) no. 1, pp. 65-89. doi: 10.4064/fm-162-1-65-89

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