Volume 4, issue 1 (2000)

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Combing Euclidean buildings

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 ${A}_{n},{B}_{n},{C}_{n}$ admits a biautomatic structure.

Keywords
Euclidean building, automatic group, combing
Primary: 20F32
Secondary: 20F10