2013/02/22 by Karel Dekimpe, Dekimpe, Karel, Gert-Jan Dugardein +1 · 1 citation
Mathematics · #Advanced Algebra and Geometry #Algebraic Topology (math.AT) #Algebraic structures and combinatorial models #FOS: Mathematics #Homotopy and Cohomology in Algebraic Topology #math.AT
paper · pdf · doi:10.48550/arxiv.1302.5512
openalex publication_date 2013/02/22 · arxiv created 2013/02/25 · arxiv updated 2013/02/26 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
In this paper we will show that for any map f on an infra-nilmanifold, the Nielsen number N(f) of this map is either equal to |L(f)|, where L(f) is the Lefschetz number of that map, or equal to the expression |L(f)-L(f+)|, where f+ is a lift of f to a 2-fold covering of that infra-nilmanifold. By exploiting the exact nature of this relationship for all powers of f, we prove that the Nielsen dynamical zeta function for a map on an infra-nilmanifold is always a rational function.