Knot theory of R-covered Anosov flows: homotopy versus isotopy of closed orbits

Abstract

In this article, we study the knots realized by periodic orbits of R-covered Anosov flows in compact 3-manifolds. We show that if two orbits are freely homotopic then in fact they are isotopic. We show that lifts of periodic orbits to the universal cover are unknotted. When the manifold is atoroidal, we deduce some finer properties regarding the existence of embedded cylinders connecting two given homotopic orbits.

20 pages, 9 figures

Cited by in corpus (2)

• Symplectic Geometry of Anosov Flows in Dimension 3 and Bi-Contact Topology
• Diversified homotopic behavior of closed orbits of some R-covered Anosov flows