Hostname: page-component-cb9f654ff-hqlzj Total loading time: 0 Render date: 2025-08-29T03:52:39.686Z Has data issue: false hasContentIssue false

Incompressible tori transverse to Anosov flows in 3-manifolds

Published online by Cambridge University Press:  17 April 2001

SÉRGIO R. FENLEY
Affiliation:
Mathematical Sciences Research Institute and University of California, Berkeley, USA

Abstract

We consider Anosov flows in 3-manifolds.Suppose that there is a rank-two free abelian subgroupof the fundamental group of the manifold, so that none of itselements can be represented by a closed orbit of the flow.We then show that the flow is topologically conjugate to a suspensionof an Anosov diffeomorphism. As a consequence we prove that if $T$is an incompressible torus so that no loop in$T$ is freely homotopic to a closed orbit of the flow,then $T$ is isotopic to a transverse torus.Finally, we show that if $T$ is an incompressible torustransverse to the stable foliation, then eitherthere is a closed leaf in the induced foliationin $T$, or the flow is topologically conjugate toa suspension Anosov flow.

Information

Type
Research Article
Copyright
1997 Cambridge University Press

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

Article purchase

Temporarily unavailable