The minimal volume orientable hyperbolic 2-cusped 3-manifolds

Author:
Ian Agol

Journal:
Proc. Amer. Math. Soc. **138** (2010), 3723-3732

MSC (2010):
Primary 57M50

DOI:
https://doi.org/10.1090/S0002-9939-10-10364-5

Published electronically:
May 12, 2010

Erratum:
Proc. Amer. Math. Soc. **75** (1979), 375.

MathSciNet review:
2661571

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Abstract | References | Similar Articles | Additional Information

Abstract: We prove that the Whitehead link complement and the pretzel link complement are the minimal volume orientable hyperbolic 3-manifolds with two cusps, with volume = 4 Catalan's constant. We use topological arguments to establish the existence of an essential surface which provides a lower bound on volume and strong constraints on the manifolds that realize that lower bound.

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Additional Information

**Ian Agol**

Affiliation:
Department of Mathematics, University of California, Berkeley, 970 Evans Hall #3840, Berkeley, California 94720-3840

Email:
ianagol@math.berkeley.edu

DOI:
https://doi.org/10.1090/S0002-9939-10-10364-5

Received by editor(s):
July 9, 2008

Received by editor(s) in revised form:
January 5, 2010

Published electronically:
May 12, 2010

Additional Notes:
The author was partially supported by NSF grant DMS-0504975 and the Guggenheim Foundation

Communicated by:
Daniel Ruberman

Article copyright:
© Copyright 2010
American Mathematical Society

The copyright for this article reverts to public domain 28 years after publication.