An averaging formula for Nielsen numbers of affine n-valued maps on infra-nilmanifolds

TL;DR

This paper extends existing formulas to compute Nielsen numbers for n-valued affine maps on infra-nilmanifolds, providing a unified averaging approach applicable to a broad class of maps.

Contribution

It introduces a generalized averaging formula for Nielsen numbers of n-valued affine maps on infra-nilmanifolds, expanding previous results from nilmanifolds.

Findings

Derived a new averaging formula for Nielsen numbers

Extended previous formulas from nilmanifolds to infra-nilmanifolds

Applicable to all n-valued affine maps on infra-nilmanifolds

Abstract

In [8,9], the authors developed a nice formula to compute the Nielsen number of a self-map on an infra-nilmanifold. For the case of nilmanifolds this formula was extended to $n$-valued maps in [4]. In this paper, we extend these results further and establish the averaging formula to compute the Nielsen number of any $n$-valued affine map on an infra-nilmanifold.