Softcover ISBN:  9780821888001 
Product Code:  CBMS/117 
141 pp 
List Price:  $44.00 
Individual Price:  $35.20 
Electronic ISBN:  9780821894422 
Product Code:  CBMS/117.E 
141 pp 
List Price:  $41.00 
MAA Member Price:  $36.90 
AMS Member Price:  $32.80 

Book DetailsCBMS Regional Conference Series in MathematicsVolume: 117; 2012MSC: Primary 20; 57;
This book presents an introduction to the geometric group theory associated with nonpositively curved cube complexes. It advocates the use of cube complexes to understand the fundamental groups of hyperbolic 3manifolds as well as many other infinite groups studied within geometric group theory.
The main goal is to outline the proof that a hyperbolic group \(G\) with a quasiconvex hierarchy has a finite index subgroup that embeds in a rightangled Artin group. The supporting ingredients of the proof are sketched: the basics of nonpositively curved cube complexes, wallspaces and dual CAT(0) cube complexes, special cube complexes, the combination theorem for special cube complexes, the combination theorem for cubulated groups, cubical smallcancellation theory, and the malnormal special quotient theorem. Generalizations to relatively hyperbolic groups are discussed. Finally, applications are described towards resolving Baumslag's conjecture on the residual finiteness of onerelator groups with torsion, and to the virtual specialness and virtual fibering of certain hyperbolic 3manifolds, including those with at least one cusp.
The text contains many figures illustrating the ideas.A copublication of the AMS and CBMS.
ReadershipGraduate students and research mathematicians interested in lowdimensional topology and geometric group theory.

Table of Contents

Chapters

Chapter 1. Overview

Chapter 2. Nonpositively curved cube complexes

Chapter 3. Cubical disk diagrams, hyperplanes, and convexity

Chapter 4. Special cube complexes

Chapter 5. Virtual specialness of malnormal amalgams

Chapter 6. Wallspaces and their dual cube complexes

Chapter 7. Finiteness properties of the dual cube complex

Chapter 8. Cubulating malnormal graphs of cubulated groups

Chapter 9. Cubical small cancellation theory

Chapter 10. Walls in cubical smallcancellation theory

Chapter 11. Annular diagrams

Chapter 12. Virtually special quotients

Chapter 13. Hyperbolicity and quasiconvexity detection

Chapter 14. Hyperbolic groups with a quasiconvex hierachy

Chapter 15. The relatively hyperbolic setting

Chapter 16. Applications


Additional Material

Request Review Copy
 Book Details
 Table of Contents
 Additional Material

 Request Review Copy
This book presents an introduction to the geometric group theory associated with nonpositively curved cube complexes. It advocates the use of cube complexes to understand the fundamental groups of hyperbolic 3manifolds as well as many other infinite groups studied within geometric group theory.
The main goal is to outline the proof that a hyperbolic group \(G\) with a quasiconvex hierarchy has a finite index subgroup that embeds in a rightangled Artin group. The supporting ingredients of the proof are sketched: the basics of nonpositively curved cube complexes, wallspaces and dual CAT(0) cube complexes, special cube complexes, the combination theorem for special cube complexes, the combination theorem for cubulated groups, cubical smallcancellation theory, and the malnormal special quotient theorem. Generalizations to relatively hyperbolic groups are discussed. Finally, applications are described towards resolving Baumslag's conjecture on the residual finiteness of onerelator groups with torsion, and to the virtual specialness and virtual fibering of certain hyperbolic 3manifolds, including those with at least one cusp.
The text contains many figures illustrating the ideas.
A copublication of the AMS and CBMS.
Graduate students and research mathematicians interested in lowdimensional topology and geometric group theory.

Chapters

Chapter 1. Overview

Chapter 2. Nonpositively curved cube complexes

Chapter 3. Cubical disk diagrams, hyperplanes, and convexity

Chapter 4. Special cube complexes

Chapter 5. Virtual specialness of malnormal amalgams

Chapter 6. Wallspaces and their dual cube complexes

Chapter 7. Finiteness properties of the dual cube complex

Chapter 8. Cubulating malnormal graphs of cubulated groups

Chapter 9. Cubical small cancellation theory

Chapter 10. Walls in cubical smallcancellation theory

Chapter 11. Annular diagrams

Chapter 12. Virtually special quotients

Chapter 13. Hyperbolicity and quasiconvexity detection

Chapter 14. Hyperbolic groups with a quasiconvex hierachy

Chapter 15. The relatively hyperbolic setting

Chapter 16. Applications