Resumen de Equivariant Nielsen invariants for discrete groups

Julia Weber

• For discrete groups G, we introduce equivariant Nielsen invariants. They are equivariant analogs of the Nielsen number and give lower bounds for the number of fixed point orbits in the G-homotopy class of an equivariant endomorphism f : X ? X. Under mild hypotheses, these lower bounds are sharp.

  We use the equivariant Nielsen invariants to show that a G-equivariant endomorphism f is G-homotopic to a fixed point free G-map if the generalized equivariant Lefschetz invariant ?G(f) is zero. Finally, we prove a converse of the equivariant Lefschetz fixed point theorem.