JournalscmhVol. 77 , No. 3DOI 10.1007/s00014-002-8348-9

Foliations, topology and geometry of 3-manifolds: R-covered foliations and transverse pseudo-Anosov flows

  • Sérgio R. Fenley

    Florida State University, Tallahassee, USA
Foliations, topology and geometry of 3-manifolds: R-covered foliations and transverse pseudo-Anosov flows cover

Abstract

We analyse the topological and geometrical behavior of foliations on 3-manifolds. We consider the transverse structure of an R-covered foliation in a 3-manifold, where R-covered means that in the universal cover the leaf space of the foliation is Hausdorff. If the manifold is aspherical we prove that either there is an incompressible torus in the manifold; or there is a transverse pseudo-Anosov flow. It follows that manifolds with R-covered foliations satisfy the weak hyperbolization conjecture.