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Hyperbolic groups.

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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 --- 51 <082> --- Mathematics--Feestbundels. Festschriften --- 51 <082> Mathematics--Feestbundels. Festschriften --- Geometric group theory. --- Hyperbolic groups. --- Groupes, Théorie géométrique des --- Groupes hyperboliques --- Geometric group theory --- Hyperbolic groups --- Groupes, Théorie géométrique des. --- Groupes hyperboliques.

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The main objective of this book is to give a broad unified introduction to the study of dimension and recurrence in hyperbolic dynamics. It includes the discussion of the foundations, main results, and main techniques in the rich interplay of four main areas of research: hyperbolic dynamics, dimension theory, multifractal analysis, and quantitative recurrence. It also gives a panorama of several selected topics of current research interest. More than half of the material appears here for the first time in book form, describing many recent developments in the area such as topics on irregular sets, variational principles, applications to number theory, measures of maximal dimension, multifractal nonrigidity, and quantitative recurrence. All the results are included with detailed proofs, many of them simplified or rewritten on purpose for the book. The text is self-contained and directed to researchers as well as graduate students that wish to have a global view of the theory together with a working knowledge of its main techniques. It will also be useful as as basis for graduate courses in dimension theory of dynamical systems, multifractal analysis, and pointwise dimension and recurrence in hyperbolic dynamics.

Differentiable dynamical systems. --- Hyperbolic groups. --- Dimension theory (Topology) --- Topology --- Group theory --- Differential dynamical systems --- Dynamical systems, Differentiable --- Dynamics, Differentiable --- Differential equations --- Global analysis (Mathematics) --- Topological dynamics --- Cell aggregation --- Global analysis (Mathematics). --- Dynamical Systems and Ergodic Theory. --- Manifolds and Cell Complexes (incl. Diff.Topology). --- Analysis. --- Mathematics. --- Analysis, Global (Mathematics) --- Differential topology --- Functions of complex variables --- Geometry, Algebraic --- Aggregation, Cell --- Cell patterning --- Cell interaction --- Microbial aggregation --- Dynamics. --- Ergodic theory. --- Manifolds (Mathematics). --- Complex manifolds. --- Mathematical analysis. --- Analysis (Mathematics). --- 517.1 Mathematical analysis --- Mathematical analysis --- Analytic spaces --- Manifolds (Mathematics) --- Geometry, Differential --- Ergodic transformations --- Continuous groups --- Mathematical physics --- Measure theory --- Transformations (Mathematics) --- Dynamical systems --- Kinetics --- Mathematics --- Mechanics, Analytic --- Force and energy --- Mechanics --- Physics --- Statics