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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Abstract
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.
| Item Type: | Article |
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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 |
| Record Number: | CaltechAUTHORS:CALgt99 |
| Persistent URL: | http://resolver.caltech.edu/CaltechAUTHORS:CALgt99 |
| Alternative URL: | http://dx.doi.org/10.2140/gt.1999.3.137 |
| Usage Policy: | No commercial reproduction, distribution, display or performance rights in this work are provided. |
| ID Code: | 1192 |
| Collection: | CaltechAUTHORS |
| Deposited By: | Archive Administrator |
| Deposited On: | 04 Jan 2006 |
| Last Modified: | 26 Dec 2012 08:43 |
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