Denis V. Osin, "Relatively Hyperbolic Groups: Intrinsic Geometry, Algebraic Properties, and Algorithmic Problems"
2005 | ISBN-10: 0821838210 | 100 pages | Djvu | 1 MB
2005 | ISBN-10: 0821838210 | 100 pages | Djvu | 1 MB
In this paper we obtain an isoperimetric characterization of relatively hyperbolicity of a groups with respect to a collection of subgroups. This allows us to apply classical combinatorial methods related to van Kampen diagrams to obtain relative analogues of some well-known algebraic and geometric properties of ordinary hyperbolic groups. We also introduce and study the notion of a relatively quasi-convex subgroup of a relatively hyperbolic group and solve some natural algorithmic problems.