Nielsen periodic point theory on infra-nilmanifolds

2015/08/18 by Gert-Jan Dugardein, Dugardein, Gert-Jan
Mathematics · #Algebraic Topology (math.AT) #Dynamical Systems (math.DS) #FOS: Mathematics #math.AT #math.DS

paper · pdf · doi:10.48550/arxiv.1508.04345

arxiv created 2015/08/18 · arxiv updated 2015/08/19

Abstract

In this paper, we expand certain aspects of Nielsen periodic point theory from tori and nilmanifolds to infra-nilmanifolds. We show that infra-nilmanifolds are essentially reducible to the GCD and essentially toral. With these structural properties in mind, we develop a method to compute the full Nielsen-Jiang number NF_n(f). We also determine for which maps it holds that NF_n(f)=N(fⁿ), for all n.

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