Equivariant Nielsen fixed point theory

Joel Better


We provide an alternative approach
to the equivariant Nielsen fixed point theory
developed by P. Wong in
[< i> Equivariant Nielsen numbers< /i> , Pacific J. Math. < b> 159< /b> (1993), 153–175] by associating an abstract simplicial complex
to any $G$-map and defining two $G$-homotopy invariants that
are lower bounds for the number of fixed points and orbits
in the $G$-homotopy class of a given $G$-map in terms of this complex.
We develop a relative equivariant Nielsen fixed point theory
along the lines above and prove a minimality result for the Nielsen-type
numbers introduced in this setting.


Equivariant fixed point theory; Nielsen fixed point theory; G-map

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