Quasiconvexity and relatively hyperbolic groups that split
Group Theory
2012-11-14 v1 Geometric Topology
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.
Cite
@article{arxiv.1211.1993,
title = {Quasiconvexity and relatively hyperbolic groups that split},
author = {Hadi Bigdely and Daniel T. Wise},
journal= {arXiv preprint arXiv:1211.1993},
year = {2012}
}