Calegari, Danny (1999) R-covered foliations of hyperbolic 3-manifolds. Geometry and Topology, 3 (6). pp. 137-153. ISSN 1465-3060. http://resolver.caltech.edu/CaltechAUTHORS:CALgt99
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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.
|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 . While writing this paper, I was partially supported by an NSF Graduate Fellowship.|
|Subject Keywords:||R-covered foliations, slitherings, hyperbolic 3-manifolds, transverse geometry|
|Usage Policy:||No commercial reproduction, distribution, display or performance rights in this work are provided.|
|Deposited By:||Archive Administrator|
|Deposited On:||04 Jan 2006|
|Last Modified:||26 Dec 2012 08:43|
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