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Journal of the American Mathematical Society
Journal of the American Mathematical Society
ISSN 1088-6834(online) ISSN 0894-0347(print)

 

Minimum volume cusped hyperbolic three-manifolds


Authors: David Gabai, Robert Meyerhoff and Peter Milley
Journal: J. Amer. Math. Soc. 22 (2009), 1157-1215
MSC (2000): Primary 57M50; Secondary 51M10, 51M25
Published electronically: May 1, 2009
MathSciNet review: 2525782
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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 $ \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.


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Additional Information

David Gabai
Affiliation: Department of Mathematics, Princeton University, Princeton, New Jersey 08544

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

DOI: http://dx.doi.org/10.1090/S0894-0347-09-00639-0
PII: S 0894-0347(09)00639-0
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.
Article copyright: © Copyright 2009 by David Gabai, Robert Meyerhoff, and Peter Milley