New York Journal of Mathematics
Volume 1 (1994-1995) 184-195


Ilya Kapovich

A Non-quasiconvex Subgroup of a Hyperbolic Group with an Exotic Limit Set

Published: December 21, 1995
Keywords: hyperbolic group, quasiconvex subgroup, limit set
Subject: Primary 20F32; Secondary 20E06

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.


This research is supported by an Alfred P. Sloan Doctoral Dissertation Fellowship

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