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Combing Euclidean buildings

Gennady A Noskov

Geometry & Topology 4 (2000) 85–116

arXiv: math.GR/0001186

Abstract

For an arbitrary Euclidean building we define a certain combing, which satisfies the “fellow traveller property” and admits a recursive definition. Using this combing we prove that any group acting freely, cocompactly and by order preserving automorphisms on a Euclidean building of one of the types An,Bn,Cn admits a biautomatic structure.

Keywords
Euclidean building, automatic group, combing
Mathematical Subject Classification 2000
Primary: 20F32
Secondary: 20F10
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Publication
Received: 9 February 1999
Revised: 10 November 1999
Accepted: 13 January 1999
Published: 28 January 2000
Proposed: Walter Neumann
Seconded: Joan Birman, Wolfgang Metzler
Authors
Gennady A Noskov
IITAM SORAN
Pevtsova 13
Omsk 644099
Russia