Published June 20, 1999
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Journal Article
Open
R-covered foliations of hyperbolic 3-manifolds
- Creators
- Calegari, Danny
Chicago
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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.
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.Files
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Additional details
- Eprint ID
- 1192
- Resolver ID
- CaltechAUTHORS:CALgt99
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