2022/06/03 by Karel Dekimpe, Dekimpe, Karel, Iris Van den Bussche +1
Computer Science · Mathematics · #Algebraic Geometry and Number Theory #Algebraic Topology (math.AT) #FOS: Mathematics #Geometry and complex manifolds #Topological and Geometric Data Analysis
paper · pdf · doi:10.48550/arxiv.2206.01581
openalex publication_date 2022/06/03 · openalex created_date 2023/02/12 · openalex updated_date 2026/07/28
In [3,9], the Nielsen zeta function Nf(z) has been shown to be rational if f is a self-map of an infra-solvmanifold of type (R). It is, however, still unknown whether Nf(z) is rational for self-maps on solvmanifolds. In this paper, we prove that Nf(z) is rational if f is a self-map of a (compact) solvmanifold of dimension ≤ 5. In any dimension, we show additionally that Nf(z) is rational if f is a self-map of an \cal NR-solvmanifold or a solvmanifold with fundamental group of the form \mathbb Zn\rtimes\mathbb Z.