Geometry & Topology

Combing Euclidean buildings

Gennady A Noskov

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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.

Article information

Source
Geom. Topol., Volume 4, Number 1 (2000), 85-116.

Dates
Received: 9 February 1999
Revised: 10 November 1999
Accepted: 13 January 1999
First available in Project Euclid: 21 December 2017

Permanent link to this document
https://projecteuclid.org/euclid.gt/1513883279

Digital Object Identifier
doi:10.2140/gt.2000.4.85

Mathematical Reviews number (MathSciNet)
MR1735633

Zentralblatt MATH identifier
1047.20031

Subjects
Primary: 20F32
Secondary: 20F10: Word problems, other decision problems, connections with logic and automata [See also 03B25, 03D05, 03D40, 06B25, 08A50, 20M05, 68Q70]

Keywords
Euclidean building automatic group combing

Citation

Noskov, Gennady A. Combing Euclidean buildings. Geom. Topol. 4 (2000), no. 1, 85--116. doi:10.2140/gt.2000.4.85. https://projecteuclid.org/euclid.gt/1513883279


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