Minimum volume cusped hyperbolic three-manifolds

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This paper is the second in a series whose goal is to understand the structure of low-volume complete orientable hyperbolic 3-manifolds. Using Mom technology, we prove that any one-cusped hyperbolic 3-manifold with volume <= 2.848 can be obtained by a Dehn filling on one of 21 cusped hyperbolic 3-manifolds. We also show how this result can be used to construct a complete list of all one-cusped hyperbolic three-manifolds with volume <= 2.848 and all closed hyperbolic three-manifolds with volume <= 0.943. In particular, the Weeks manifold is the unique smallest volume closed orientable hyperbolic 3-manifold.
57 pages, 14 figures

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Geometric Topology, 57M50 (Primary) 51M10, 51M25 (Secondary)

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http://salesiana.dossiersoluciones.com/handle/123456789/129625

Consulte el texto completo en el siguiente enlace:

https://arxiv.org/abs/0705.4325
 http://arxiv.org/abs/0705.4325

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arXiv