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Hyperbolic groups.

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Hyperbolic spaces. --- Hyperbolic groups. --- Espaces hyperboliques --- Groupes hyperboliques --- Hyperbolic spaces --- Hyperbolic groups --- Espaces hyperboliques. --- Groupes hyperboliques.

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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.

Hyperbolic groups. --- Group theory. --- 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.

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Topological groups. Lie groups --- Hyperbolic groups. --- Groupes hyperboliques --- Tiling (Mathematics) --- Pavage (mathématiques) --- Cancellation theory (Group theory) --- Hyperbolic groups --- Combinatorial designs and configurations --- Mathematics --- Group theory --- Groupes hyperboliques.

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Group theory --- Geometry --- Combinatorial set theory --- Combinatorische groepentheorie --- Geometry [Hyperbolic ] --- Groupes [Theories des ] combinatoires --- Géométrie hyperbolique --- Meetkunde [Hyperbolische ] --- Hyperbolic groups. --- 51 --- Hyperbolic groups --- Mathematics --- 51 Mathematics --- Geometric group theory --- Groupes, Théorie géométrique des --- Groupes, Théorie des --- Géometrie hyperbolique