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ISSN (electronic): 1364-0380
ISSN (print): 1465-3060
$\mathbb{R}$–covered foliations of hyperbolic 3-manifolds

Danny Calegari

Geometry & Topology 3 (1999) 137–153

arXiv: math.GT/9808064

Abstract

We produce examples of taut foliations of hyperbolic 3–manifolds which are –covered but not uniform — ie the leaf space of the universal cover is , but pairs of leaves are not contained in bounded neighborhoods of each other. This answers in the negative a conjecture of Thurston. We further show that these foliations can be chosen to be C0 close to foliations by closed surfaces. Our construction underscores the importance of the existence of transverse regulating vector fields and cone fields for –covered foliations. Finally, we discuss the effect of perturbing arbitrary –covered foliations.

Keywords
$\mathbb{R}$–covered foliations, slitherings, hyperbolic 3–manifolds, transverse geometry
Mathematical Subject Classification
Primary: 57M50, 57R30
Secondary: 53C12
References
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Publication
Received: 1 September 1998
Revised: 9 April 1999
Accepted: 14 June 1999
Published: 20 June 1999
Proposed: David Gabai
Seconded: Walter Neumann, Cameron Gordon
Authors
Danny Calegari
Department of Mathematics
University of California at Berkeley
Berkeley
California 94720
USA