Topology and Geometric Group Theory Seminar
Tuesday, February 15, 2022 - 1:00pm
Malott 206
We study homeomorphisms of an irreducible three-manifold which preserve a surface and restrict to a dynamically interesting homeomorphism of that surface. Specifically, we would like to know when that dynamically interesting behavior extends to the rest of the
three-manifold.
Rodriguez-Hertz, Rodriguez-Hertz and Ures showed that when the surface S is a torus, and "dynamically interesting" means Anosov, then the three-manifold must be a torus bundle over a circle, and the homeomorphism is isotopic rel S to a homeomorphism which is Anosov on every fiber.
I'll explain their result and talk about a generalization to higher-dimensional surfaces.
This is joint work in progress with Christoforos Neofytidis.