Equivariant Nielsen invariants for discrete groups

Details Equivariant Nielsen invariants for discrete groups Equivariant Nielsen invariants for discrete groups

2006-06-22

arxiv.org/abs/math/0606561v1

Mathematics

Algebraic Topology

17 pages, submitted to Pacific Journal of Mathematics

Scientific paper

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 of f is zero. Finally, we prove a converse of the equivariant Lefschetz fixed point theorem.

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