Seminar

Speaker: Ellis Buckminster     Title: Foliations forcing closed orbits

Abstract: Knowing topological and geometric properties about foliations on 3-manifolds often yields dynamical information about transverse flows, and vice versa. In this vein, we address the following question: What properties of a foliation force all transverse flows to have closed orbits? We fully resolve this question in the case of depth one foliations on closed hyperbolic 3-manifolds, showing roughly that foliations of “intermediate complexity” admit transverse flows without closed orbits, while the most simple and most complicated foliations force closed orbits. This is joint work with Audrey Rosevear.

Speaker: Ross Griebenow        Title: Hyperbolization of fibered 3-manifolds

Abstract: We sketch Thurston's proof that a 3-manifold fibering over the circle admits a hyperbolic structure if and only if the manifold is atoroidal.