Nielsen numbers of selfmaps of flat 3-manifolds
type: Item
instance of: scholarly article
title: Nielsen numbers of selfmaps of flat 3-manifolds
zbMATH Open document ID: 1297.55005
author: Xuezhi Zhao
author: Daciberg Lima Gonçalves
author: Peter Wong
published in: Bulletin of the Belgian Mathematical Society - Simon Stevin
publication date: 2014-06-19T00:00:00Z
full work available at URL: https://projecteuclid.org/euclid.bbms/1400592619
review text: 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.
Mathematics Subject Classification ID: 55M20
Mathematics Subject Classification ID: 20H15
zbMATH DE Number: 6305490
zbMATH Keywords: Nielsen number
zbMATH Keywords: homeomorphism, flat 3-manifold
zbMATH Keywords: fundamental group
zbMATH Keywords: Jiang condition
reviewed by: Christian Fenske
MaRDI profile type: Publication
description: scientific article; zbMATH DE number 6305490