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.
"Reidemeister spectra for solvmanifolds in low dimensions." Topol. Methods Nonlinear Anal. 53 (2) 575 - 601, 2019. https://doi.org/10.12775/TMNA.2019.012