Nielsen zeta functions on infra-nilmanifolds up to dimension three

TL;DR

This paper classifies all self-maps on infra-nilmanifolds up to dimension three and computes their Nielsen zeta functions, providing a comprehensive understanding of their dynamical properties.

Contribution

It systematically enumerates all self-maps on low-dimensional infra-nilmanifolds and explicitly calculates their Nielsen zeta functions, filling a gap in the literature.

Findings

Complete list of self-maps on infra-nilmanifolds up to dimension three.

Explicit Nielsen zeta functions for each map.

Enhanced understanding of dynamical behaviors on these manifolds.

Abstract

In this paper, we will list all possible self-maps on infra-nilmanifolds up to dimension three and we will give the Nielsen zeta function for any of those maps.