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  • Open Daily: 10am - 10pm
    Alley-side Pickup: 10am - 7pm

    3038 Hennepin Ave Minneapolis, MN
    612-822-4611

Open Daily: 10am - 10pm | Alley-side Pickup: 10am - 7pm
3038 Hennepin Ave Minneapolis, MN
612-822-4611
Hyperbolic Manifolds and Discrete Groups

Hyperbolic Manifolds and Discrete Groups

Kapovich, Michael

Paperback

Series: Modern Birkhäuser Classics

AlgebraGeneral MathematicsGeometry

ISBN10: 0817649123
ISBN13: 9780817649128
Publisher: Springer Nature
Published: Oct 28 2009
Pages: 470
Weight: 1.52
Height: 1.00 Width: 6.14 Depth: 9.21
Language: English
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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