Geometry & Topology

Combing Euclidean buildings

Gennady A Noskov

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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

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

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

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Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

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

Euclidean building automatic group combing


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

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