On Quasiconvexity and Relative Hyperbolic Structures
Group Theory
2011-05-03 v4
Abstract
Let G be a group which is hyperbolic relative to a collection of subgroups A, and it is also hyperbolic relative to a collection of subgroups B. Suppose that the collection A contains B. We characterize, for subgroups of G, when quasicovexity relative to A implies quasiconvexity relative to B. We also show that quasiconvexity relative to B implies quasiconvexity relative to A. Some applications are discussed.
Cite
@article{arxiv.0811.2384,
title = {On Quasiconvexity and Relative Hyperbolic Structures},
author = {Eduardo Martinez-Pedroza},
journal= {arXiv preprint arXiv:0811.2384},
year = {2011}
}
Comments
Version to appear in Geometriae Dedicata. Included version of Bounded Coset Penetration for general relatively hyperbolic groups, two figures, and updated references