Geometry and Topology Seminar: "Endperiodic maps, foliation cones, and pseudo-Anosov flows"

Abstract: Endperiodic automorphisms of surfaces arise as monodromies of noncompact leaves in depth one foliations of 3-manifolds. In the early 90s Handel and Miller studied these maps and proved that they exhibit much of the behavior of automorphisms of finite type surfaces, as described by the Nielsen-Thurston classification. Their work did not appear in print, but recently Cantwell, Conlon, and Fenley published a detailed account which plays a key part in Cantwell and Conlon's work on foliation cones. These foliation cones are analogues of Thurston's fibered cones, but in the setting of sutured manifolds. In this talk I will introduce endperiodic maps and foliation cones, and describe some new results connecting them to pseudo-Anosov flows in closed 3-manifolds. This is joint work in progress with Samuel Taylor and Yair Minsky.