Minimum volume cusped hyperbolic three-manifolds

David Gabai; Robert Meyerhoff; Peter Milley

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arXiv · 0705.4325

Minimum volume cusped hyperbolic three-manifolds

David Gabai·Robert Meyerhoff·Peter Milley

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Abstract

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.

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BibTeX RIS

David Gabai, Robert Meyerhoff, Peter Milley. 2007-05-30. Minimum volume cusped hyperbolic three-manifolds. https://arxiv.org/abs/0705.4325

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