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Hairdressing in groups: a survey of combings and formal languages

Sarah Rees

Geometry & Topology Monographs 1 (1998) 493–509

DOI: 10.2140/gtm.1998.1.493

arXiv: math.GR/9810201

Abstract

A group is combable if it can be represented by a language of words satisfying a fellow traveller property; an automatic group has a synchronous combing which is a regular language. This article surveys results for combable groups, in particular in the case where the combing is a formal language.

Dedicated to David Epstein on the occasion of his 60th birthday.

Keywords

combings, formal languages, fellow travellers, automatic groups

Mathematical Subject Classification

Primary: 20-04, 20F10, 68Q40

Secondary: 03D40

References
Publication

Received: 15 November 1997
Published: 29 October 1998

Authors
Sarah Rees
University of Newcastle
Newcastle NE1 7RU
United Kingdom