Minimum volume cusped hyperbolic three-manifolds
Geometric Topology
2007-05-31 v1
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.
Keywords
Cite
@article{arxiv.0705.4325,
title = {Minimum volume cusped hyperbolic three-manifolds},
author = {David Gabai and Robert Meyerhoff and Peter Milley},
journal= {arXiv preprint arXiv:0705.4325},
year = {2007}
}