Nielsen numbers of $n$-valued maps on infra-solvmanifolds

TL;DR

This paper develops a formula to compute Nielsen numbers for multi-valued maps on infra-solvmanifolds by relating them to coincidence numbers of single-valued maps on solvmanifolds, advancing topological fixed point theory.

Contribution

It introduces a novel formula for Nielsen numbers of n-valued maps on infra-solvmanifolds, linking them to Nielsen coincidence numbers on solvmanifolds.

Findings

Derived a formula for Nielsen numbers of n-valued maps on infra-solvmanifolds.

Expressed Nielsen numbers in terms of coincidence numbers of single-valued maps.

Extended Nielsen fixed point theory to multi-valued maps on complex manifolds.

Abstract

We derive a formula for the Nielsen number $N(f)$ for every $n$-valued self-map $f$ of an infra-solvmanifold. To do this, we express $N(f)$ in terms of Nielsen coincidence numbers of single-valued maps on solvmanifolds, and derive a formula for Nielsen coincidence numbers in that setting.