A non-quasiconvex subgroup of a hyperbolic group with an exotic limit set. (English) Zbl 0879.20015

Kapovich, Ilya

New York J. Math. 1, 184-195 (1995).

Summary: 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.

MSC:

20F65	Geometric group theory
20E07	Subgroup theorems; subgroup growth
20F05	Generators, relations, and presentations of groups
20E06	Free products of groups, free products with amalgamation, Higman-Neumann-Neumann extensions, and generalizations

Keywords:

hyperbolic groups; quasiconvex subgroups; limit sets; freely indecomposable finitely presented subgroups