Geometry & Topology, Vol. 4 (2000) Paper no. 2, pages 85--116.

Combing Euclidean buildings

Gennady A Noskov

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

AMS subject classification. Primary: 20F32. Secondary: 20F10.

DOI: 10.2140/gt.2000.4.85

E-print: arXiv:math.GR/0001186

Submitted to GT on 9 February 1999. (Revised 10 November 1999.) Paper accepted 13 January 2000. Paper published 28 January 2000.

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Gennady A Noskov
Russia, 644099, Omsk
Pevtsova 13, IITAM SORAN
Email: noskov@private.omsk.su

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