English

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.

Keywords

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

R2 v1 2026-06-21T11:41:47.425Z