descriptionPublicationkeyboard_double_arrow_right Article , Preprint , Other literature type 01 Jun 2013Embargo end date: 01 Jan 2012Publisher:Michigan Mathematical JournalJournal:Michigan Mathematical Journal, volume 62 (issn: 0026-2285,

Authors: Bigdely, Hadi; Wise, Daniel T.;

doi: 10.1307/mmj/1370870378 , 10.48550/arxiv.1211.1993

arXiv: http://arxiv.org/abs/1211.1993

Quasiconvexity and relatively hyperbolic groups that split

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Abstract

We explore the combination theorem for a group G splitting as a graph of relatively hyperbolic groups. Using the fine graph approach to relative hyperbolicity, we find short proofs of the relative hyperbolicity of G under certain conditions. We then provide a criterion for the relative quasiconvexity of a subgroup H depending on the relative quasiconvexity of the intersection of H with the vertex groups of G. We give an application towards local relative quasiconvexity.

Keywords

20F06, Mathematics - Geometric Topology, FOS: Mathematics, Geometric Topology (math.GT), Group Theory (math.GR), Mathematics - Group Theory

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