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Shrinkwrapping and the taming of hyperbolic 3-manifolds

Calegari, Danny and Gabai, David (2006) Shrinkwrapping and the taming of hyperbolic 3-manifolds. Journal of the American Mathematical Society, 19 (2). pp. 385-446. ISSN 0894-0347. doi:10.1090/S0894-0347-05-00513-8.

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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:Copyright 2005, by Danny Calegari and David Gabai. Received by editor(s): June 22, 2004. The first author is grateful to Nick Makarov for some useful analytic discussions. The second author is grateful to Michael Freedman for many long conversations in Fall 1996 which introduced him to the Tame Ends conjecture. He thanks Francis Bonahon, Yair Minsky and Jeff Brock for their interest and helpful comments. Part of this research was carried out while he was visiting Nara Women’s University, the Technion and the Institute for Advanced Study. He thanks them for their hospitality. We thank the referees for their many thoughtful suggestions and comments.
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Subject Keywords:generated kleinian groups; positive ricci curvature; minimal-surfaces; noncompact 3-manifolds; compact submanifolds; variational problems; sufficiently large; manifolds; boundary; topology
Issue or Number:2
Record Number:CaltechAUTHORS:20090414-123644599
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Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:13972
Deposited By: Joy Painter
Deposited On:14 Apr 2009 21:25
Last Modified:08 Nov 2021 22:42

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