Geometry & Topology, Vol. 3 (1999)
Paper no. 6, pages 137--153.
R-covered foliations of hyperbolic 3-manifolds
Danny Calegari
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.
Keywords.
R-covered foliations, slitherings, hyperbolic 3-manifolds, transverse geometry
AMS subject classification.
Primary: 57M50, 57R30.
Secondary: 53C12.
DOI: 10.2140/gt.1999.3.137
E-print: arXiv:math.GT/9808064
Submitted to GT on 1 September 1998.
(Revised 9 April 1999.)
Paper accepted 14 June 1999.
Paper published 20 June 1999.
Notes on file formats
Danny Calegari
Department of Mathematics
UC Berkeley
Berkeley, CA 94720
Email: dannyc@math.berkeley.edu
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