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Hyperbolic spaces. --- Hyperbolic groups. --- Espaces hyperboliques --- Groupes hyperboliques --- Hyperbolic spaces --- Hyperbolic groups --- Espaces hyperboliques. --- Groupes hyperboliques.
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Automorphic forms. --- Hyperbolic spaces. --- Topology. --- Formes automorphes. --- Espaces hyperboliques. --- Topologie.
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Chaotic behavior in systems --- Differentiable dynamical systems --- Hyperbolic spaces
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Over the past three decades there has been a total revolution in the classic branch of mathematics called 3-dimensional topology, namely the discovery that most solid 3-dimensional shapes are hyperbolic 3-manifolds. This book introduces and explains hyperbolic geometry and hyperbolic 3- and 2-dimensional manifolds in the first two chapters and then goes on to develop the subject. The author discusses the profound discoveries of the astonishing features of these 3-manifolds, helping the reader to understand them without going into long, detailed formal proofs. The book is heavily illustrated with pictures, mostly in color, that help explain the manifold properties described in the text. Each chapter ends with a set of exercises and explorations that both challenge the reader to prove assertions made in the text, and suggest further topics to explore that bring additional insight. There is an extensive index and bibliography.
Three-manifolds (Topology) --- Geometry, Hyperbolic. --- Complex manifolds. --- Hyperbolic spaces.
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Geometry, Hyperbolic --- Hyperbolic spaces --- Géométrie hyperbolique --- Espaces hyperboliques --- Géométrie hyperbolique
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This classic book is at the crossroads of several branches of mathematics: hyperbolic geometry, discrete groups, 3-dimensional topology, geometric group theory, and complex analysis. The main focus throughout the text is on Thurston's hyperbolization theorem, one of the central results of 3-dimensional topology that has completely changed the landscape of the field. The book contains a number of open problems and conjectures related to the hyperbolization theorem as well as rich discussions on related topics including geometric structures on 3-manifolds, higher dimensional negatively curved manifolds, and hyperbolic groups. Featuring beautiful illustrations, a rich set of examples, numerous exercises, and an extensive bibliography and index, Hyperbolic Manifolds and Discrete Groups continues to serve as an ideal graduate text and comprehensive reference. The book is very clearly written and fairly self-contained. It will be useful to researchers and advanced graduate students in the field and can serve as an ideal guide to Thurston's work and its recent developments. ---Mathematical Reviews Beyond the hyperbolization theorem, this is an important book which had to be written; some parts are still technical and will certainly be streamlined and shortened in the next years, but together with Otal's work a complete published proof of the hyperbolization theorem is finally available. Apart from the proof itself, the book contains a lot of material which will be useful for various other directions of research. ---Zentralbatt MATH This book can act as source material for a postgraduate course and as a reference text on the topic as the references are full and extensive. ... The text is self-contained and very well illustrated. ---ASLIB Book Guide
Group theory --- Differential topology --- Topology --- Geometry --- wiskunde --- geometrie --- topologie --- Hyperbolic spaces --- Discrete groups
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Differential geometry. Global analysis --- Diffeomorphisms --- Hyperbolic spaces --- Manifolds (Mathematics) --- Geometry, Differential --- Topology --- Hyperbolic complex manifolds --- Manifolds, Hyperbolic complex --- Spaces, Hyperbolic --- Geometry, Non-Euclidean --- Differential topology --- Diffeomorphisms. --- Difféomorphismes. --- Hyperbolic spaces. --- Espaces hyperboliques.
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Geometry --- Geometry, Hyperbolic. --- Géométrie hyperbolique. --- Hyperbolic spaces. --- Espaces hyperboliques. --- Spectral theory (Mathematics) --- Théorie spectrale (mathématiques) --- Asymptotic expansions. --- Développements asymptotiques. --- Asymptotic expansions --- Geometry, Hyperbolic --- Hyperbolic spaces --- Functional analysis --- Hilbert space --- Measure theory --- Transformations (Mathematics) --- Hyperbolic complex manifolds --- Manifolds, Hyperbolic complex --- Spaces, Hyperbolic --- Geometry, Non-Euclidean --- Hyperbolic geometry --- Lobachevski geometry --- Lobatschevski geometry --- Asymptotic developments --- Asymptotes --- Convergence --- Difference equations --- Divergent series --- Functions --- Numerical analysis
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