Tame combings, almost convexity and rewriting systems for groups
type: Item
instance of: scholarly article
title: Tame combings, almost convexity and rewriting systems for groups
zbMATH Open document ID: 0873.20023
DOI: 10.1007/PL00004311
author: Susan Hermiller
author: John Meier
published in: Mathematische Zeitschrift
publication date: 1997-11-02T00:00:00Z
review text: A finite complete rewriting system for a group is a finite presentation which gives an algorithmic solution to the word problem. Finite complete rewriting systems have proven to be useful objects in geometric group theory, yet little is known about the geometry of groups admitting such rewriting systems. We show that a group \(G\) with a finite complete rewriting system admits a tame 1-combing; it follows (by work of Mihalik and Tschantz) that if \(G\) is an infinite fundamental group of a closed irreducible 3-manifold \(M\), then the universal cover of \(M\) is \(\mathbb{R}^3\). We also establish that a group admitting a geodesic rewriting system is almost convex in the sense of Cannon, and that almost convex groups are tame 1-combable.
Mathematics Subject Classification ID: 20F10
Mathematics Subject Classification ID: 57M05
Mathematics Subject Classification ID: 20F65
Mathematics Subject Classification ID: 20F05
Mathematics Subject Classification ID: 20F34
zbMATH DE Number: 1033933
zbMATH Keywords: finite complete rewriting systems
zbMATH Keywords: finite presentations
zbMATH Keywords: algorithmic solutions
zbMATH Keywords: word problem
zbMATH Keywords: geometry of groups
zbMATH Keywords: tame 1-combings
zbMATH Keywords: fundamental groups
zbMATH Keywords: closed irreducible 3-manifolds
zbMATH Keywords: universal covers
zbMATH Keywords: geodesic rewriting systems
zbMATH Keywords: almost convex groups
MaRDI profile type: Publication
full work available at URL: pl00004311
OpenAlex ID: W1983964871
description: scientific article; zbMATH DE number 1033933