Height in splittings of hyperbolic groups

Details Height in splittings of hyperbolic groups Height in splittings of hyperbolic groups

2004-03-08

arxiv.org/abs/math/0403125v1

Proc. Indian Acad. Sci. (Math. Sci.), Vol. 114, No. 1, February 2004, pp. 39-54

Mathematics

Group Theory

16 pages, no figures, no tables

Scientific paper

Suppose $H$ is a hyperbolic subgroup of a hyperbolic group $G$. Assume there exists $n > 0$ such that the intersection of $n$ essentially distinct conjugates of $H$ is always finite. Further assume $G$ splits over $H$ with hyperbolic vertex and edge groups and the two inclusions of $H$ are quasi-isometric embeddings. Then $H$ is quasiconvex in $G$. This answers a question of Swarup and provides a partial converse to the main theorem of \cite{GMRS}.

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