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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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Pubblicazione: | Princeton, New Jersey : , : Princeton University Press, , [2021] |
©2021 | |
Descrizione fisica: | 1 online resource (376 p.) : 166 color illus |
Disciplina: | 512.2 |
Soggetto topico: | Hyperbolic groups |
Group theory | |
Soggetto non controllato: | CAT(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 | |
Nota di bibliografia: | Includes bibliographical references and index. |
Nota di contenuto: | 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 |
Sommario/riassunto: | 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. |
Titolo autorizzato: | The structure of groups with a quasiconvex hierarchy ![]() |
ISBN: | 0-691-21350-X |
Formato: | Materiale a stampa ![]() |
Livello bibliografico | Monografia |
Lingua di pubblicazione: | Inglese |
Record Nr.: | 9910554261903321 |
Lo trovi qui: | Univ. Federico II |
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