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

 

Lower bounds on volumes of hyperbolic Haken 3-manifolds


Authors: Ian Agol, Peter A. Storm and William P. Thurston; with an appendix by Nathan Dunfield
Journal: J. Amer. Math. Soc. 20 (2007), 1053-1077
MSC (2000): Primary 58Jxx, 57Mxx
Published electronically: May 31, 2007
MathSciNet review: 2328715
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Abstract: We prove a volume inequality for 3-manifolds having $ C^{0}$ metrics ``bent'' along a surface and satisfying certain curvature conditions. The result makes use of Perelman's work on the Ricci flow and geometrization of closed 3-manifolds. Corollaries include a new proof of a conjecture of Bonahon about volumes of convex cores of Kleinian groups, improved volume estimates for certain Haken hyperbolic 3-manifolds, and a lower bound on the minimal volume of orientable hyperbolic 3-manifolds. An appendix compares estimates of volumes of hyperbolic 3-manifolds drilled along a closed embedded geodesic with experimental data.


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Additional Information

Ian Agol
Affiliation: Department of Mathematics, Computer Science, and Statistics, University of Illinois at Chicago, 322 SEO, m/c 249, 851 S. Morgan St., Chicago, Illinois 60607-7045
Address at time of publication: Department of Mathematics, University of California at Berkeley, 970 Evans Hall #3840, Berkeley, California 94720-3840
Email: agol@math.uic.edu, ianagol@gmail.com

Peter A. Storm
Affiliation: Department of Mathematics, Stanford University, Building 380, 450 Serra Mall, Stanford, California 94305-2125
Email: storm@math.stanford.edu

William P. Thurston
Affiliation: Department of Mathematics, Cornell University, 310 Malott Hall, Ithaca, New York 14853-4201
Email: wpt@math.cornell.edu

Nathan Dunfield
Affiliation: Department of Mathematics, 253-37, Caltech, Pasadena, California 91125
Address at time of publication: (August 1, 2007) Department of Mathematics, University of Illinois at Urbana-Champaign, 1409 W. Green Street, Urbana, Illinois 61801
Email: dunfield@caltech.edu, nathan@dunfield.info

DOI: http://dx.doi.org/10.1090/S0894-0347-07-00564-4
PII: S 0894-0347(07)00564-4
Received by editor(s): June 30, 2005
Published electronically: May 31, 2007
Additional Notes: The first author was partially supported by NSF grant DMS-0204142 and the Sloan Foundation
The second author was partially supported by an NSF postdoctoral fellowship
The third author was partially supported by the NSF grant DMS-0343694
The last author was partially supported by the NSF grant DMS-0405491 and the Sloan foundation
Article copyright: © Copyright 2007 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.