THE LEFSCHETZ NUMBER OF AN n-VALUED MULTIMAP

Robert F. Brown (U. S. A.)

Received January 19, 2007

Abstract

An n-valued multimap is a continuous multivalued function such that is an unordered subset of n points of Y for each If X and Y are finite polyhedra, then f induces a graded homomorphism of homology with rational coefficients. For the Lefschetz number of f is defined to be the Lefschetz number of the induced homomorphism. If then every n-valued multimap homotopic to f has a fixed point. If X is the circle, then the Lefschetz number of f is related to the Nielsen number of Schirmer as in the single-valued case, that is,

Keywords and phrases: n-valued multimap, simplicial approximation, Lefschetz fixed point theorem, Nielsen number.