5 research outputs found
Quasiconvexity and relatively hyperbolic groups that split
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