### A fixed point index for equivariant maps

DOI: http://dx.doi.org/10.12775/TMNA.1999.017

#### 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.

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.

#### Keywords

Nielsen number; equivariant fixed point index

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