Reidemeister spectra for solvmanifolds in low dimensions

TL;DR

This paper computes the Reidemeister spectra for all fundamental groups of low-dimensional solvmanifolds, providing a comprehensive classification of their twisted conjugacy class structures.

Contribution

It determines the Reidemeister spectra for all solvmanifold fundamental groups up to Hirsch length 4, extending understanding of their algebraic and topological properties.

Findings

Reidemeister spectra are fully classified for low-dimensional solvmanifolds.

The spectra reveal distinct conjugacy class structures in these groups.

Results facilitate further studies in fixed point theory and geometric group theory.

Abstract

The Reidemeister number of an endomorphism of a group is the number of twisted conjugacy classes determined by that endomorphism. The collection of all Reidemeister numbers of all automorphisms of a group $G$ is called the Reidemeister spectrum of $G$. In this paper, we determine the Reidemeister spectra of all fundamental groups of solvmanifolds up to Hirsch length 4.