Commentarii Mathematici Helvetici
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Foliations, topology and geometry of 3-manifolds: R-covered foliations and transverse pseudo-Anosov flowsSérgio R. Fenley (1) Department of Mathematics, Florida State University, 208 James J. Love Building, FL 32306-4510, TALLAHASSEE, UNITED STATES
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.
Keywords: Foliations, transverse flows, geometric structures on leaves, holonomy, transverse structure of foliation, universal circle, Gromov hyperbolic
Fenley S. Foliations, topology and geometry of 3-manifolds: R-covered foliations and transverse pseudo-Anosov flows. Comment. Math. Helv. 77 (2002), 415-490. doi: 10.1007/s00014-002-8348-9