R-covered foliations of hyperbolic 3-manifolds
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
Cite
@article{arxiv.math/9808064,
title = {R-covered foliations of hyperbolic 3-manifolds},
author = {Danny Calegari},
journal= {arXiv preprint arXiv:math/9808064},
year = {2014}
}
Comments
17 pages. Published copy, also available at http://www.maths.warwick.ac.uk/gt/GTVol3/paper6.abs.html