# ePrints

## Regularity of Quasigeodesics in a hyperbolic group

Lookup NU author(s): Professor Sarah Rees

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### Abstract

We prove that for $\lambda \geq 1$ and all sufficiently large $\epsilon$, the set of \Le-quasigeodesics in an infinite word-hyperbolic group $G$ is regular if and only if $\lambda$ is rational. In fact, this set of quasigeodesics defines an asynchronous automatic structure for $G$. We also introduce the idea of an {\em exact} \Le-quasigeodesic and show that for rational $\lambda$ and appropriate $\epsilon$ the sets of exact \Le-quasigeodesics define synchronous automatic structures.

Author(s): Rees SE; Holt D

Publication type: Article

Publication status: Published

Journal: International Journal of Algebra and Computation

Year: 2003

Volume: 13

Issue: 5

Pages: 585-596

ISSN (print): 0218-1967

ISSN (electronic): 1793-6500

Publisher: World Scientific Publishing Co. Pte. Ltd.

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