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Overview"The main goal of the book is to present a proof of the following. Thurston's Hyperbolization Theorem (""The Big Monster""). Suppose that M is a compact atoroidal Haken 3-manifold that has zero Euler characteristic. Then the interior of M admits a complete hyperbolic metric of finite volume. This theorem establishes a strong link between the geometry and topology 3 of 3-manifolds and the algebra of discrete subgroups of Isom(JH[ ). It completely changed the landscape of 3-dimensional topology and theory of Kleinian groups. Further, it allowed one to prove things that were beyond the reach of the standard 3-manifold technique as, for example, Smith's conjecture, residual finiteness of the fundamental groups of Haken manifolds, etc. In this book we present a complete proof of the Hyperbolization Theorem in the ""generic case."" Initially we planned 1 including a detailed proof in the remaining case of manifolds fibered over § as well. However, since Otal's book [Ota96] (which treats the fiber bundle case) became available, only a sketch of the proof in the fibered case will be given here." Full Product DetailsAuthor: Michael KapovichPublisher: Birkhauser Boston Inc Imprint: Birkhauser Boston Inc Edition: 2001 Dimensions: Width: 15.50cm , Height: 2.50cm , Length: 23.50cm Weight: 1.520kg ISBN: 9780817649128ISBN 10: 0817649123 Pages: 470 Publication Date: 28 October 2009 Audience: Professional and scholarly , Professional & Vocational Format: Paperback Publisher's Status: Active Availability: In Print  This item will be ordered in for you from one of our suppliers. Upon receipt, we will promptly dispatch it out to you. For in store availability, please contact us. Table of ContentsThree-Dimensional Topology.- Thurston Norm.- Geometry of Hyperbolic Space.- Kleinian Groups.- Teichmüller Theory of Riemann Surfaces.- to Orbifold Theory.- Complex Projective Structures.- Sociology of Kleinian Groups.- Ultralimits of Metric Spaces.- to Group Actions on Trees.- Laminations, Foliations, and Trees.- Rips Theory.- Brooks’ Theorem and Circle Packings.- Pleated Surfaces and Ends of Hyperbolic Manifolds.- Outline of the Proof of the Hyperbolization Theorem.- Reduction to the Bounded Image Theorem.- The Bounded Image Theorem.- Hyperbolization of Fibrations.- The Orbifold Trick.- Beyond the Hyperbolization Theorem.ReviewsThis 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 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 We recommend the excellent introduction of the present book for the history of the various contributions, and also for a sketch of the proof itself... This is an important book which had to be written ... the book contains a lot of material which will be useful for various other directions of research. --Zentralblatt 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 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 We recommend the excellent introduction of the present book for the history of the various contributions, and also for a sketch of the proof itself... This is an important book which had to be written ... the book contains a lot of material which will be useful for various other directions of research. -Zentralblatt 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 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 We recommend the excellent introduction of the present book for the history of the various contributions, and also for a sketch of the proof itself... This is an important book which had to be written ... the book contains a lot of material which will be useful for various other directions of research. --Zentralblatt Math Author InformationTab Content 6Author Website:Countries AvailableAll regions |
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