Equivariant Nielsen fixed point theory

Abstract

We provide an alternative approach to the equivariant Nielsen fixed point theory developed by P. Wong in [Equivariant Nielsen numbers, Pacific J. Math. 159 (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.