Nielsen periodic point theory on infra-nilmanifolds

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 $N{F}_n(f)$. We also determine for which maps it holds that $N{F}_n(f)=N(f^n)$, for all $n$.