A Lefschetz type coincidence theorem

TL;DR

This paper establishes a Lefschetz-type coincidence theorem linking the coincidence index and Lefschetz number for maps between topological spaces and manifolds, generalizing known results and providing conditions for the existence of coincidence points.

Contribution

It introduces a generalized Lefschetz-type coincidence theorem applicable to arbitrary topological spaces and manifolds, extending classical results in fixed point theory.

Findings

Coincidence index equals Lefschetz number under the theorem's conditions

Non-zero Lefschetz number guarantees a coincidence point

Contains known results for manifolds and acyclic fibers cases

Abstract

A Lefschetz-type coincidence theorem for two maps f,g:X->Y from an arbitrary topological space X to a manifold Y is given: I(f,g)=L(f,g), the coincidence index is equal to the Lefschetz number. It follows that if L(f,g) is not equal to zero then there is an x in X such that f(x)=g(x). In particular, the theorem contains some well-known coincidence results for (i) X,Y manifolds and (ii) f with acyclic fibers.