Complexes of non-positive curvature and automorphisms of the 4-punctured sphere
type: Item
instance of: scholarly article
title: Complexes of non-positive curvature and automorphisms of the 4-punctured sphere
zbMATH Open document ID: 0867.57003
DOI: 10.1007/BF01268933
author: Thomas Brady
published in: Archiv der Mathematik
publication date: 1996-10-27T00:00:00Z
review text: The author considers extensions of free groups \(F_3\) of rank three by \(\mathbb{Z}\) which can be realized as the fundamental group of the mapping torus of a 4-punctured sphere automorphism. There is a deformation retraction of the mapping torus to a 2-complex which carries a metric of non-positive curvature and the groups considered act cocompactly by isometries on the 2-complex thus giving a new proof of fact that these extension have automatic structures. A similar approach was used by the author to obtain such a result of \(\mathbb{Z}\)-extensions of rank two free groups.
Mathematics Subject Classification ID: 57M05
Mathematics Subject Classification ID: 20F65
Mathematics Subject Classification ID: 20F34
zbMATH DE Number: 938590
zbMATH Keywords: automatic structure
zbMATH Keywords: fundamental group
zbMATH Keywords: mapping torus
zbMATH Keywords: 2-complex
reviewed by: Gerhard Burde
MaRDI profile type: Publication
cites work: Complexes of nonpositive curvature for extensions of \(F_ 2\) by \(\mathbb{Z}\)
cites work: Automorphism groups of punctured surfaces
cites work: Q4003861
cites work: Small cancellation theory and automatic groups
full work available at URL: https://doi.org/10.1007/bf01268933
OpenAlex ID: W1968221586
description: scientific article; zbMATH DE number 938590