Minimum volume cusped hyperbolic three-manifolds
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- by David Gabai, Robert Meyerhoff and Peter Milley;
- J. Amer. Math. Soc. 22 (2009), 1157-1215
- DOI: https://doi.org/10.1090/S0894-0347-09-00639-0
- Published electronically: May 1, 2009
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 $\le 2.848$ 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 $3$-manifolds with volume $\le 2.848$ and all closed hyperbolic $3$-manifolds with volume $\le 0.943$. In particular, the Weeks manifold is the unique smallest volume closed orientable hyperbolic $3$-manifold.References
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Bibliographic Information
- David Gabai
- Affiliation: Department of Mathematics, Princeton University, Princeton, New Jersey 08544
- MR Author ID: 195365
- Robert Meyerhoff
- Affiliation: Department of Mathematics, Boston College, Chestnut Hill, Massachusetts 02467
- Peter Milley
- Affiliation: Department of Mathematics and Statistics, University of Melbourne, Melbourne, Australia
- Received by editor(s): August 14, 2008
- Published electronically: May 1, 2009
- Additional Notes: The first author was partially supported by NSF grants DMS-0554374 and DMS-0504110.
THe second author was partially supported by NSF grants DMS-0553787 and DMS-0204311.
The third author was partially supported by NSF grant DMS-0554624 and by ARC Discovery grant DP0663399. - © Copyright 2009 by David Gabai, Robert Meyerhoff, and Peter Milley
- Journal: J. Amer. Math. Soc. 22 (2009), 1157-1215
- MSC (2000): Primary 57M50; Secondary 51M10, 51M25
- DOI: https://doi.org/10.1090/S0894-0347-09-00639-0
- MathSciNet review: 2525782