Infinitely many hyperbolic 3-manifolds which contain no Reebless foliation

71 citations recorded by the source corpus.

How researchers see this paper

The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.

Laminations and groups of homeomorphisms of the circle (2002, unknown): “Examples of hyperbolic manifolds without taut foliations were already known from the breakthrough work of Roberts, Shareshian, and Stein [RSS].”
Foliations and the Geometry of 3-Manifolds (2007, background): “In a tour de force, Roberts, Shareshian and Stein give examples in [209] of some hyperbolic 3-manifold groups which admit no nontrivial actions on simplyconnected 1-manifolds.”
Heegaard Floer homology and genus one, one‐boundary component open books (2008, methodology): “In [1], we use this result to produce an infinite family of hyperbolic 3-manifolds with no co-orientable taut foliations, extending the first known set of such 3-manifolds, which was discovered by Roberts, Shareshian, and Stein among fillings of punctured torus bundles [ 47 ].”
Pseudo-Anosov flows in toroidal manifolds (2010, methodology): “Previous study of group actions on order trees and related sets was done by Roberts and Stein [44] and Roberts, Shareshian and Stein [43] with some exceptional consequences for the existence of foliations in certain 3–manifolds.”
Monopoles and lens space surgeries (2003, methodology): “) The first examples of hyperbolic three-manifolds which admit no taut foliation were constructed in [37], see also [6] In the interest of concreteness, we include the following:”