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Shrinkwrapping and the taming of hyperbolic 3-manifolds

Author(s): Danny Calegari; David Gabai
Journal: J. Amer. Math. Soc. 19 (2006), 385-446.
MSC (2000): Primary 57M50, 57N10; Secondary 30F40, 49F10
Posted: December 7, 2005
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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: 10.1090/S0894-0347-05-00513-8
PII: S 0894-0347(05)00513-8
Received by editor(s): June 22, 2004
Posted: 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
Copyright of article: Copyright 2005, by Danny Calegari and David Gabai

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The following works have cited this article

Kapovich, Ilya and Weidmann, Richard, Kleinian groups and the rank problem., Geometry and Topology 9 (2005), 375--402. MR MR2140986 (2006d:20079)

Myers, Robert, End reductions, fundamental groups, and covering spaces of irreducible open 3-manifolds., Geometry and Topology 9 (2005), 971--990. MR MR2140996 (2006c:57014)

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