Relatively hyperbolic groups : intrinsic geometry, algebraic properties, and algorithmic problems / Denis V. Osin.

Format:

Book

Author/Creator:

Osin, Denis V., 1974- author.

Series:

Memoirs of the American Mathematical Society ; no. 843.

Memoirs of the American Mathematical Society, 0065-9266 ; number 843

Language:

English

Subjects (All):

Geometric group theory.

Hyperbolic groups.

Physical Description:

1 online resource (114 p.)

Edition:

1st ed.

Place of Publication:

Providence, Rhode Island : American Mathematical Society, 2006.

Language Note:

English

Summary:

In this the authors obtain an isoperimetric characterization of relatively hyperbolicity of a groups with respect to a collection of subgroups. This allows them 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. There is also an introduction and study of the notion of a relatively quasi-convex subgroup of a relatively hyperbolic group and solve somenatural algorithmic problems.

Contents:

""Contents""; ""Chapter 1. Introduction""; ""1.1. Preliminary remarks""; ""1.2. Main results""; ""Chapter 2. Relative isoperimetric inequalities""; ""2.1. Relative presentations and length functions""; ""2.2. Geometry of van Kampen diagrams over relative presentations""; ""2.3. Relative Dehn functions""; ""2.4. Splitting Theorem for relatively finitely presented groups""; ""2.5. Isoperimetric functions of Cayley graphs""; ""Chapter 3. Geometry of finitely generated relatively hyperbolic groups""; ""3.1. Conventions and notation""; ""3.2. Properties of quasi�geodesics""

""3.3. Geodesic triangles in Cayley graphs""""3.4. Symmetric geodesies""; ""Chapter 4. Algebraic properties""; ""4.1. Elements of finite order""; ""4.2. Relatively quasi�convex subgroups""; ""4.3. Cyclic subgroups and translation numbers""; ""Chapter 5. Algorithmic problems""; ""5.1. The word and membership problems""; ""5.2. The parabolicity problems""; ""5.3. Algorithmic problems for hyperbolic elements""; ""Open questions""; ""Appendix. Equivalent definitions of relative hyperbolicity""; ""Bibliography""

Notes:

"Volume 179, number 843 (second of 5 numbers)."

Includes bibliographical references.

Description based on print version record.

ISBN:

1-4704-0444-3