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."

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9780817649128

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Reviews

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

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

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