Sergio Fenley
Florida State University
Title
Exotic codimension one Anosov flows
Abstract
Anosov flows are flows that admit invariant stable and unstable bundles, which are respectively contracted or expanded when flowing forward. The Verjosky conjecture states that every codimension one Anosov flow in dimensions 4 or higher is orbitally equivalent to a suspension Anosov flow. Codimension one means that either the weak stable or the weak unstable foliation of the flow has codimension one. This conjecture is 50 years old. In joint work with K. Mann and R. Potrie, we construct infinitely many counterexamples to the conjecture in 4-manifolds. To achieve that, we need a closed hyperbolic 3-manifold M, a faithful minimal representation of \pi_1(M) into Homeo+(S^1) (the circle), and a group equivariant Cannon-Thurston map f from S^1 to the sphere at infinity of hyperbolic 3-space. With this data we can construct a topological Anosov flow in dimension 4. If the set of non injective points of the map f has image in the sphere at infinity which has measure zero, we show how to perturb the topological Anosov flow to obtain a (smooth) Anosov flow, which is orbitally equivalent to it. We then show that there are infinitely many examples satisfying the data, producing counterexamples to the Verjovsky conjecture.
In addition, there will be a pre-talk for graduate students in the same location at 2:15 pm
