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R-covered foliations of hyperbolic 3-manifolds

Calegari, Danny (1999) R-covered foliations of hyperbolic 3-manifolds. Geometry and Topology, 3 (6). pp. 137-153. ISSN 1465-3060. doi:10.2140/gt.1999.3.137.

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We produce examples of taut foliations of hyperbolic 3-manifolds which are R-covered but not uniform --- ie the leaf space of the universal cover is R, but pairs of leaves are not contained in bounded neighborhoods of each other. This answers in the negative a conjecture of Thurston `Three-manifolds, foliations and circles I' (math.GT/9712268). We further show that these foliations can be chosen to be C^0 close to foliations by closed surfaces. Our construction underscores the importance of the existence of transverse regulating vector fields and cone fields for R-covered foliations. Finally, we discuss the effect of perturbing arbitrary R-covered foliations.

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Additional Information:Proposed: David Gabai; Seconded: Walter Neumann, Cameron Gordon. Received: 1 September 1998; Revised: 9 April 1999; Published: 20 June 1999 In writing this paper I benefited from numerous helpful conversations with Andrew Casson, Sergio Fenley and Bill Thurston. In particular, many of the ideas contained here are either implicit or explicit in the wonderful paper [7]. While writing this paper, I was partially supported by an NSF Graduate Fellowship.
Subject Keywords:R-covered foliations, slitherings, hyperbolic 3-manifolds, transverse geometry
Issue or Number:6
Record Number:CaltechAUTHORS:CALgt99
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Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:1192
Deposited By: Archive Administrator
Deposited On:04 Jan 2006
Last Modified:08 Nov 2021 19:08

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