Elder Siblings and the Taming of Hyperbolic 3-Manifolds

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Elder Siblings and the Taming of Hyperbolic 3-Manifolds

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Title: Elder Siblings and the Taming of Hyperbolic 3-Manifolds
Author: Freedman, Michael H.; McMullen, Curtis T.

Note: Order does not necessarily reflect citation order of authors.

Citation: Freedman, Michael H. and Curtis T. McMullen. 1998. Elder siblings and the taming of hyperbolic 3-manifolds. Annales Academiae Scientiarum Fennicae 23: 415–428. Revised 2003.
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Abstract: A 3-manifold is tame if it is homeomorphic to the interior of a compact manifold with boundary. Marden’s conjecture asserts that any hyperbolic 3-manifold \(\mathbb{M} = \mathbb{H}^3/\Gamma\) with \(\pi_1(M)\) finitely-generated is tame. This paper presents a criterion for tameness. We show that wildness of \(\mathbb{M}\) is detected by large-scale knotting of orbits of \(\Gamma\). The elder sibling property prevents knotting and implies tameness by a Morse theory argument. We also show the elder sibling property holds for all convex cocompact groups and a strict form of it characterizes such groups.
Published Version: http://www.acadsci.fi/mathematica/
Other Sources: http://www.math.harvard.edu/~ctm/papers/index.html
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Citable link to this page: http://nrs.harvard.edu/urn-3:HUL.InstRepos:3446000
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