GT seminar: "Symplectic geometry of Anosov flows in dimension three"

Abstract: In this talk, I will illustrate how symplectic geometry can be leveraged in the study of uniformly hyperbolic dynamics. Namely, every Anosov flow on a three-manifold M has an associated non-Weinstein Liouville domain V=[-1,1]xM, whose invariants (e.g. symplectic cohomology, Rabinowitz-Floer cohomology, wrapped Fukaya category) are homotopy invariants of the flow. Moreover, every orbit of the flow gives an exact Lagrangian cylinder, all of which are nontrivial and independent of each other in the Fukaya category, such that the A_infty category they generate does not satisfy Abouzaid’s generation criterion, in contrast to the Weinstein case. Time permitting, I will discuss the classical algebraic cases, their symplectic invariants, and further results concerning closed Lagrangians.

This is a talk in our geometry and topology seminar series.