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Outline of the Proof of the Hyperbolization Theorem

  • Michael Kapovich
Chapter
Part of the Modern Birkhäuser Classics book series (MBC)

Abstract

Finally, we can present an outline of the proof of Thurston's Hyperbolization Theorem. Our discussion mainly follows [Mor84]. By Theorem 8.36, it is enough to prove the Hyperbolization Theorem for a finite covering of M. Thus we will consider only compact orientable pared manifolds (M, P), which contain orientable superincompressible surfaces and where \(P=\partial M\) is the designated parabolic locus. Thurston's theorem is proven by induction on levels of the Haken hierarchy of M. It turns out that the main problem in proving Theorem 1.42 is the last step of the induction.

Keywords

Hyperbolic Manifold Kleinian Group Hyperbolic Structure Teichmiiller Space Hyperbolic Orbifold 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Birkhäuser Boston 2009

Authors and Affiliations

  1. 1.Department of MathematicsUniversity of California, DavisDavisU.S.A.

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