Borsuk-Ulam theorem, fixed point index and chain approximations for maps with multiplicity

Abstract

In this article we consider m-acyclic maps with respect to a field F and prove the existence of chain approximation for such maps. Furthermore we provide a unified approach to the Borsuk-Ulam theorem and the Bourgin-Yang generalization. Finally we prove the existence of ^-systems for certain m-acyclic maps and define a fixed point index.