From riches to raags : 3manifolds, rightangled artin groups, and cubical geometry
 Responsibility
 Daniel T. Wise.
 Publication
 Providence, Rhode Island : Published for the Conference Board of the Mathematical Sciences by the American Mathematical Society, Providence, Rhode Island with support from the National Science Foundation, [2012]
 Physical description
 xiii, 141 pages : color illustrations ; 26 cm.
 Series
 Regional conference series in mathematics ; no. 117.
Access
Available online
Science Library (Li and Ma)
Stacks
Call number  Status 

QA1 .R33 NO.117  Unknown 
More options
Creators/Contributors
 Author/Creator
 Wise, Daniel T., 1971
Contents/Summary
 Bibliography
 Includes bibliographical references (pages 135138) and index.
 Contents

 Overview
 Nonpositively curved cube complexes
 Cubical disk diagrams, hyperplanes, and convexity
 Special cube complexes
 Virtual specialness of malnormal amalgams
 Wallspaces and their dual cube complexes
 Finiteness properties of the dual cube complex
 Cubulating malnormal graphs of cubulated groups
 Cubical smallcancellation theory Walls in cubical smallcancellation theory
 Annular diagrams
 Virtually special quotients
 Hyperbolicity and quasiconvexity detection
 Hyperbolic groups with a quasiconvex hierarchy
 The relatively hyperbolic setting
 Applications.
 Publisher's Summary
 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.
(source: Nielsen Book Data)9780821888001 20160615
Subjects
 Subject
 Hyperbolic groups.
 Group theory.
 Group theory and generalizations  Special aspects of infinite or finite groups  Hyperbolic groups and nonpositively curved groups.
 Group theory and generalizations  Special aspects of infinite or finite groups  Cancellation theory; application of van Kampen diagrams.
 Manifolds and cell complexes  Lowdimensional topology  None of the above, but in this section.
Bibliographic information
 Publication date
 2012
 Series
 CBMS Regional conference series in mathematics ; number 117
 ISBN
 9780821888001 (pbk. : acidfree paper)
 0821888005 (pbk. : acidfree paper)