Memoirs of the American Mathematical Society 2006; 100 pp; softcover Volume: 179 ISBN10: 0821838210 ISBN13: 9780821838211 List Price: US$68 Individual Members: US$40.80 Institutional Members: US$54.40 Order Code: MEMO/179/843
 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 wellknown algebraic and geometric properties of ordinary hyperbolic groups. We also introduce and study the notion of a relatively quasiconvex subgroup of a relatively hyperbolic group and solve some natural algorithmic problems. Table of Contents  Introduction
 Relative isoperimetric inequalities
 Geometry of finitely generated relatively hyperbolic groups
 Algebraic properties
 Algorithmic problems
 Open questions
 Appendix. Equivalent definitions of relative hyperbolicity
 Bibliography
