Relatively Hyperbolic Groups: Intrinsic Geometry, Algebraic Properties, and Algorithmic Problems: Intrinsic Geometry, Algebraic Properties, and Algorithmic Problems

· American Mathematical Society 843 巻 · American Mathematical Soc.
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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.

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