-covered foliations and transverse pseudo-Anosov flows in atoroidal pieces
Sergio R. Fenley
Florida State University, Tallahassee, USA
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Abstract
We study the transverse geometric behavior of 2-dimensional foliations in 3-manifolds. We show that an -covered, transversely orientable foliation with Gromov hyperbolic leaves in a closed 3-manifold admits a regulating, transverse pseudo-Anosov flow (in the appropriate sense) in each atoroidal piece of the manifold. The flow is a blow up of a one prong pseudo-Anosov flow. In addition we show that there is a regulating flow for the whole foliation. We also determine how deck transformations act on the universal circle of the foliation.
Cite this article
Sergio R. Fenley, -covered foliations and transverse pseudo-Anosov flows in atoroidal pieces. Comment. Math. Helv. 98 (2023), no. 1, pp. 1–39
DOI 10.4171/CMH/547