From riches to raags : 3-manifolds, right-angled artin groups, and cubical geometry
- Daniel T. Wise.
- 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, 
- Physical description
- xiii, 141 pages : color illustrations ; 26 cm.
- Regional conference series in mathematics ; no. 117.
Science Library (Li and Ma)
|QA1 .R33 NO.117||Unknown|
- Wise, Daniel T., 1971-
- Includes bibliographical references (pages 135-138) and index.
- 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 small-cancellation theory --Walls in cubical small-cancellation theory
- Annular diagrams
- Virtually special quotients
- Hyperbolicity and quasiconvexity detection
- Hyperbolic groups with a quasiconvex hierarchy
- The relatively hyperbolic setting
- 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 3-manifolds 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 right-angled 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 small-cancellation 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 one-relator groups with torsion, and to the virtual specialness and virtual fibering of certain hyperbolic 3-manifolds, including those with at least one cusp. The text contains many figures illustrating the ideas.
(source: Nielsen Book Data)9780821888001 20160615
- 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 -- Low-dimensional topology -- None of the above, but in this section.
- Publication date
- CBMS Regional conference series in mathematics ; number 117
- 9780821888001 (pbk. : acid-free paper)
- 0821888005 (pbk. : acid-free paper)
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