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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
Published electronically: May 12, 2010
Erratum: Proc. Amer. Math. Soc. 75 (1979), 375.
MathSciNet review: 2661571
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Abstract: We prove that the Whitehead link complement and the $ (-2,3,8)$ pretzel link complement are the minimal volume orientable hyperbolic 3-manifolds with two cusps, with volume $ 3.66...$ = 4 $ \times$ 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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Ian Agol
Affiliation: Department of Mathematics, University of California, Berkeley, 970 Evans Hall #3840, Berkeley, California 94720-3840

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.

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