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