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Hyperbolic Manifolds And Discrete Groups (Modern Birkhuser Classics),Used
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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 3manifold 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 3manifolds and the algebra of discrete subgroups of Isom(JH[ ). It completely changed the landscape of 3dimensional topology and theory of Kleinian groups. Further, it allowed one to prove things that were beyond the reach of the standard 3manifold 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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