Abstract
In this section we discuss various conjectures related to Thurston’s Hyperbolization Theorem. Our discussion is far from being comprehensive. We refer the interested reader to Kirby’s list of problems [Kir97] for more details.
Some hypotheses of the Hyperbolization Theorem are necessary for the hyperbolicity of the 3-manifold M (e.g., being atoroidal); others are not. Most importantly, the assumption that M is Haken (conjecturally) should be replaced by the assumption that M is irreducible and has infinite fundamental group.
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© 2009 Birkhäuser Boston
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Kapovich, M. (2009). Beyond the Hyperbolization Theorem. In: Hyperbolic Manifolds and Discrete Groups. Modern Birkhäuser Classics. Birkhäuser Boston. https://doi.org/10.1007/978-0-8176-4913-5_20
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DOI: https://doi.org/10.1007/978-0-8176-4913-5_20
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Online ISBN: 978-0-8176-4913-5
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