Equivariant Nielsen invariants for discrete groups

2006/06/22 by Julia Weber, Weber, Julia · 2 citations
Mathematics · Medicine · #54H25 #55M20 #57R91 (Primary) #57S99 (Secondary) #Algebraic Topology (math.AT) #FOS: Mathematics #Geometric and Algebraic Topology #Homotopy and Cohomology in Algebraic Topology #Ophthalmology and Eye Disorders #math.AT #msc:54H25 #msc:55M20 #msc:57R91 #msc:57S99

paper · pdf · doi:10.48550/arxiv.math/0606561

17 pages, submitted to Pacific Journal of Mathematics

arxiv created 2006/06/22 · openalex publication_date 2006/06/22 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

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.

Citations

• The Universal Functorial Equivariant Lefschetz Invariant

Cited by

• On the Klein and Williams Conjecture for the Equivariant Fixed Point Problem
• Functoriality of the Klein-Williams Invariant and Universality Theory

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