Geometry & Topology 4 (2000) 85–116

DOI: 10.2140/gt.2000.4.85

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 A_n, B_n, C_n admits a biautomatic structure.

Keywords

Euclidean building, automatic group, combing

Mathematical Subject Classification

Primary: 20F32

Secondary: 20F10

References

Forward citations

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