Height in splittings of hyperbolic groups

2004/03/08 by Mahan Mitra
Mathematics · #math.GR #math.MG #msc:20F32 #msc:57M50

paper · pdf

published as Proc. Indian Acad. Sci. (Math. Sci.), Vol. 114, No. 1, February 2004, pp. 39-54 · 16 pages, no figures, no tables

arxiv created 2004/03/08 · arxiv updated 2009/12/01

Abstract

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 \citeGMRS.

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