04104nam 2200673 450 991055426190332120230630001139.00-691-21350-X10.1515/9780691213507(CKB)4100000011807718(DE-B1597)570994(DE-B1597)9780691213507(MiAaPQ)EBC6512276(Au-PeEL)EBL6512276(OCoLC)1241449093(EXLCZ)99410000001180771820211007d2021 uy 0engur||#||||||||txtrdacontentcrdamediacrrdacarrierThe structure of groups with a quasiconvex hierarchy /Daniel T. WisePrinceton, New Jersey :Princeton University Press,[2021]©20211 online resource (376 p.) 166 color illusAnnals of Mathematics Studies ;3960-691-17045-2 0-691-17044-4 Includes bibliographical references and index.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 --IndexThis 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.Annals of Mathematics StudiesHyperbolic groupsGroup theoryCAT(0).Gromov.Thurston.geometric group theory.graphs of groups.hierarchies.hyperbolic groups.one relator groups.relatively hyperbolic groups.small cancellation theory.subgroup separability.virtual haken.word hyperbolic groups.Hyperbolic groups.Group theory.512.2Wise Daniel T.1971-521402MiAaPQMiAaPQMiAaPQBOOK9910554261903321The structure of groups with a quasiconvex hierarchy2820041UNINA