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The Structure of Groups with a Quasiconvex Hierarchy: (AMS-209)
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The Structure of Groups with a Quasiconvex Hierarchy: (AMS-209) (Paperback)

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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 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.

Science & MathematicsMathematicsGeometryScience & MathematicsMathematicsGroups & group theoryScience & MathematicsMathematicsTopology Publisher: Princeton University Press Publication Date: 09/02/2021 ISBN-13: 9780691170459  Details: Type: Paperback Format: Books
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Daniel T. Wise is James McGill Professor in the Department of Mathematics and Statistics at McGill University. His previous book is From Riches to Raags: 3-Manifolds, Right-Angled Artin Groups, and Cubical Geometry.

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