A fixed point index for equivariant maps

Abstract

The purpose of the paper is to define a fixed point index for equivariant maps of $G$-ENR's and to state and prove some of its properties, such as the compactly fixed $G$-homotopy property, the Lefschetz property, its converse, and the retraction property. At the end, some examples are given of equivariant self-maps which have a nonzero index (hence cannot be deformed equivariantly to be fixed point free) but have a zero $G$-Nielsen invariant.