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Relatively Hyperbolic Groups: Intrinsic Geometry, Algebraic Properties, and Algorithmic Problems
Denis V. Osin, City College (CUNY), New York, NY

Memoirs of the American Mathematical Society
2006; 100 pp; softcover
Volume: 179
ISBN-10: 0-8218-3821-0
ISBN-13: 978-0-8218-3821-1
List Price: US$68
Individual Members: US$40.80
Institutional Members: US$54.40
Order Code: MEMO/179/843
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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.

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
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