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

   

 

Shrinkwrapping and the taming of hyperbolic 3-manifolds


Authors: Danny Calegari and David Gabai
Journal: J. Amer. Math. Soc. 19 (2006), 385-446
MSC (2000): Primary 57M50, 57N10; Secondary 30F40, 49F10
Published electronically: December 7, 2005
MathSciNet review: 2188131
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Abstract: We introduce a new technique for finding CAT$ (-1)$ surfaces in hyperbolic 3-manifolds. We use this to show that a complete hyperbolic 3-manifold with finitely generated fundamental group is geometrically and topologically tame.


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Additional Information

Danny Calegari
Affiliation: Department of Mathematics, Caltech, Pasadena, California 91125

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

DOI: http://dx.doi.org/10.1090/S0894-0347-05-00513-8
PII: S 0894-0347(05)00513-8
Received by editor(s): June 22, 2004
Published electronically: December 7, 2005
Additional Notes: The first author was partially supported by Therese Calegari and NSF grant DMS-0405491
The second author was partially supported by NSF grant DMS-0071852
Article copyright: © Copyright 2005 by Danny Calegari and David Gabai