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Record Nr. |
UNINA9910554261903321 |
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Autore |
Wise Daniel T. <1971-> |
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Titolo |
The structure of groups with a quasiconvex hierarchy / / Daniel T. Wise |
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Pubbl/distr/stampa |
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Princeton, New Jersey : , : Princeton University Press, , [2021] |
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©2021 |
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ISBN |
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Descrizione fisica |
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1 online resource (376 p.) : 166 color illus |
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Collana |
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Annals of Mathematics Studies ; ; 396 |
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Disciplina |
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Soggetti |
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Hyperbolic groups |
Group theory |
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Lingua di pubblicazione |
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Formato |
Materiale a stampa |
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Livello bibliografico |
Monografia |
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Nota di bibliografia |
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Includes bibliographical references and index. |
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Nota di contenuto |
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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 |
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Sommario/riassunto |
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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 |
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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. |
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