Commentarii Mathematici Helvetici
Full-Text PDF (662 KB) | Metadata | Table of Contents | CMH summary
Published online: 2002-09-30
Foliations, topology and geometry of 3-manifolds: R-covered foliations and transverse pseudo-Anosov flowsSérgio R. Fenley (1) Florida State University, Tallahassee, USA
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 Sérgio: 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