An example of a non-quasiconvex subgroup of a word hyperbolic group with exotic limit set

1995/06/29 by Ilya Kapovich, Kapovich, Ilya
Mathematics · #Advanced Algebra and Geometry #FOS: Mathematics #Geometric and Algebraic Topology #Group Theory (math.GR) #Mathematical Dynamics and Fractals #math.GR

paper · pdf · doi:10.48550/arxiv.math/9506207

AMS-Tex, 5 pages, no figures. Submitted to New York J. Math

arxiv created 1995/06/29 · openalex publication_date 1995/06/29 · arxiv updated 2009/11/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We construct an example of a torsion free freely indecomposable finitely presented non-quasiconvex subgroup H of a word hyperbolic group G such that the limit set of H is not the limit set of a quasiconvex subgroup of G. In particular, this gives a counterexample to the conjecture of G.Swarup that a finitely presented one-ended subgroup of a word hyperbolic group is quasiconvex if and only if it has finite index in its virtual normalizer.

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