Beyond the Hyperbolization Theorem
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.
KeywordsFundamental Group Hyperbolic Manifold Hyperbolic Group Klein Bottle Nonpositive Curvature
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