One relator groups are semistable at infinity
type: Item
instance of: scholarly article
title: One relator groups are semistable at infinity
zbMATH Open document ID: 0789.57003
DOI: 10.1016/0040-9383(92)90010-F
author: M. Mihalik
author: S. Tschantz
published in: Topology
publication date: 1993-05-16T00:00:00Z
review text: Finitely generated 1-relator groups form an important class of groups of cohomological dimension 2. By an inductive argument with groups which either split as amalgamated free products or HNN-extensions the authors show that their 1-relator groups \(G\) are semistable at infinity. (This means that any two proper rays converging to the same end of some universal \(G\)-space are properly homotopic.) This result implies the important corollary that \(H^ 2(G,\mathbb{Z} G)\) is free abelian.
Mathematics Subject Classification ID: 57M05
Mathematics Subject Classification ID: 57S17
Mathematics Subject Classification ID: 20J99
Mathematics Subject Classification ID: 55R40
zbMATH DE Number: 167785
zbMATH Keywords: finitely generated 1-relator groups
zbMATH Keywords: groups of cohomological dimension 2
zbMATH Keywords: amalgamated free products
zbMATH Keywords: HNN-extensions
zbMATH Keywords: semistable at infinity
zbMATH Keywords: \(H^ 2(G,\mathbb{Z} G)\)
reviewed by: Charles B. Thomas
MaRDI profile type: Publication
full work available at URL: 0040-9383(92)90010-f
OpenAlex ID: W2009064741
description: scientific article; zbMATH DE number 167785