Equivariant Nielsen fixed point theory - Better, Joel (Topological Methods in Nonlinear Analysis, 2010)
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.