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Regularity of quasigeodesics in a hyperbolic group

Lookup NU author(s): Professor Sarah Rees

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Abstract

We prove that for λ ≥ 1 and all sufficiently large ε, the set of (λ, ε)-quasigeodesics in an infinite word-hyperbolic group G is regular if and only if A is rational. In fact, this set of quasigeodesics defines an asynchronous automatic structure for G. We also introduce the idea of an exact (λ, ε)-quasigeodesic and show that for rational A and appropriate ε the sets of exact (λ, ε)-quasigeodesics define synchronous automatic structures.

Publication metadata

Author(s): Holt DF, Rees S

Publication type: Article

Publication status: Published

Journal: International Journal of Algebra and Computation

Year: 2003

Volume: 13

Issue: 5

Pages: 585-596

Print publication date: 01/10/2003

ISSN (print): 0218-1967

ISSN (electronic): 1793-6500

Publisher: World Scientific Publishing

URL: http://dx.doi.org/10.1142/S0218196703001560

DOI: 10.1142/S0218196703001560

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