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 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.
Citation
Danny Calegari. "$\mathbb{R}$–covered foliations of hyperbolic 3-manifolds." Geom. Topol. 3 (1) 137 - 153, 1999. https://doi.org/10.2140/gt.1999.3.137
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