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

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

1995-06-29

arxiv.org/abs/math/9506207v1

Mathematics

Group Theory

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

Scientific paper

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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