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.
- ISBN13 9780821838211
- Publish Date 1 December 2006
- Publish Status Active
- Publish Country US
- Imprint American Mathematical Society
- Edition illustrated Edition
- Format Paperback
- Pages 100
- Language English