Infinitely many hyperbolic 3-manifolds which contain no Reebless foliation

We investigate group actions on simply-connected (second countable but not necessarily Hausdorff) 1-manifolds and describe an infinite family of closed hyperbolic 3-manifolds whose fundamental groups do not act nontrivially on such 1-manifolds. As a corollary we conclude that these 3-manifolds contain no Reebless foliation. In fact, these arguments extend to actions on oriented R R -order trees and hence these 3-manifolds contain no transversely oriented essential lamination; in particular, they are non-Haken.