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arXiv · 1211.1993

Quasiconvexity and relatively hyperbolic groups that split

Hadi Bigdely·Daniel T. Wise
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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.

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Hadi Bigdely, Daniel T. Wise. 2012-11-08. Quasiconvexity and relatively hyperbolic groups that split. https://arxiv.org/abs/1211.1993

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