The Structure of Groups with a Quasiconvex Hierarchy : : (AMS-209) / / Daniel T. Wise.

• Superior document: Title is part of eBook package: De Gruyter EBOOK PACKAGE COMPLETE 2021 English
• VerfasserIn: Wise, Daniel T.,
• Place / Publishing House: Princeton, NJ : : Princeton University Press, , [2021]; ©2021
• Year of Publication: 2021
• Language: English
• Series: Annals of Mathematics Studies ; 366
• Physical Description: 1 online resource (376 p.) :; 166 color illus.
• Other title: Frontmatter --; Contents --; Acknowledgments --; Chapter One Introduction --; Chapter Two CAT(0) Cube Complexes --; Chapter Three Cubical Small-Cancellation Theory --; Chapter Four Torsion and Hyperbolicity --; Chapter Five New Walls and the B(6) Condition --; Chapter Six Special Cube Complexes --; Chapter Seven Cubulations --; Chapter Eight Malnormality and Fiber-Products --; Chapter Nine Splicing Walls --; Chapter Ten Cutting X ∗ --; Chapter Eleven Hierarchies --; Chapter Twelve Virtually Special Quotient Theorem --; Chapter Thirteen Amalgams of Virtually Special Groups --; Chapter Fourteen Large Fillings Are Hyperbolic and Preservation of Quasiconvexity --; Chapter Fifteen Relatively Hyperbolic Case --; Chapter Sixteen Largeness and Omnipotence --; Chapter Seventeen Hyperbolic 3-Manifolds with a Geometrically Finite Incompressible Surface --; Chapter Eighteen Limit Groups and Abelian Hierarchies --; Chapter Nineteen Application Towards One-Relator Groups --; Chapter Twenty Problems --; References --; Index
• Format: Mode of access: Internet via World Wide Web.
• ISBN: 9780691213507; 9783110754001; 9783110753776; 9783110754131; 9783110753905; 9783110494914; 9783110739121
• DOI: 10.1515/9780691213507?locatt=mode:legacy
• Access: restricted access
• Hierarchical level: Monograph
• Statement of Responsibility: Daniel T. Wise.

This monograph on the applications of cube complexes constitutes a breakthrough in the fields of geometric group theory and 3-manifold topology. Many fundamental new ideas and methodologies are presented here for the first time, including a cubical small-cancellation theory generalizing ideas from the 1960s, a version of Dehn Filling that functions in the category of special cube complexes, and a variety of results about right-angled Artin groups. The book culminates by establishing a remarkable theorem about the nature of hyperbolic groups that are constructible as amalgams.The applications described here include the virtual fibering of cusped hyperbolic 3-manifolds and the resolution of Baumslag's conjecture on the residual finiteness of one-relator groups with torsion. Most importantly, this work establishes a cubical program for resolving Thurston's conjectures on hyperbolic 3-manifolds, and validates this program in significant cases. Illustrated with more than 150 color figures, this book will interest graduate students and researchers working in geometry, algebra, and topology.