UNSPECIFIED (2001) Computation in word-hyperbolic groups. INTERNATIONAL JOURNAL OF ALGEBRA AND COMPUTATION, 11 (4). pp. 467-487. ISSN 0218-1967

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Abstract

We describe two practical algorithms for computing with word-hyperbolic groups, both of which we have implemented. The first is a method for estimating the maximum width, if it exists, of geodesic bigons in the Cayley graph of a finitely presented group G. Our procedure will terminate if and only this maximum width exists, and it has been proved by Papasoglu that this is the case if and only if G is word-hyperbolic. So the algorithm amounts to a method of verifying the property of word-hyperbolicity of G. The aim of the second algorithm is to compute the thinness constant for geodesic triangles in the Cayley graph of G. This seems to be a much more difficult problem, but our implementation does succeed with straightforward examples. Both algorithms involve substantial computations with finite state automata.

Item Type:	Journal Article
Subjects:	Q Science > QA Mathematics
Journal or Publication Title:	INTERNATIONAL JOURNAL OF ALGEBRA AND COMPUTATION
Publisher:	WORLD SCIENTIFIC PUBL CO PTE LTD
ISSN:	0218-1967
Date:	August 2001
Volume:	11
Number:	4
Number of Pages:	21
Page Range:	pp. 467-487
Publication Status:	Published
URI:	http://wrap.warwick.ac.uk/id/eprint/11705

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