### Regularity of Quasigeodesics in a hyperbolic group (2003)

Author(s): Rees SE; Holt D

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.

• Journal: International Journal of Algebra and Computation
• Volume: 13
• Issue: 5
• Pages: 585-596
• Publisher: World Scientific Publishing Co. Pte. Ltd.
• Publication type: Article
• Bibliographic status: Published
 Professor Sarah Rees Professor of Pure Mathematics Email: sarah.rees@ncl.ac.uk Telephone: +44 (0) 191 208 7236