Nielsen numbers of selfmaps of flat 3-manifolds
A subgroup \(\pi\) of the group of homeomorphisms of \(\mathbb{R}^n\) is crystallographic if it is a discrete uniform subgroup, it is Bieberbach if in addition it is torsion free. A flat \(n\)-manifold is the quotient of \(\mathbb{R}^n\) by a Bieberbach group. According to \textit{J. A. Wolf} [Spaces of constant curvature. 3rd ed. Boston, Mass.: Publish or Perish, Inc. (1974; Zbl 0281.53034)] there are ten flat 3-manifolds. The authors explicitly compute the Nielsen numbers of a self-homeomorphism for each of these manifolds and they compute the Nielsen number for arbitrary self-maps.
scientific article; zbMATH DE number 6305490