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

Full-text PDF Free Access

Abstract | References | Similar Articles | Additional Information

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

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