Joint IAS/Princeton University Symplectic Geometry Seminar

An Anosov flow $\Phi$ on a closed $3$-manifold $M$ gives rise to a non-Weinstein Liouville structure on $V:=[-1,1] \times M$. Building upon the work of Hozoori, we establish a homotopy correspondence between Anosov flows and certain pairs of contact forms. Moreover, the symplectic invariants of $V$ only depend on the \emph{homotopy class of $\Phi$}. We focus on a subcategory $\mathcal{W}_0$ of the wrapped Fukaya category of $V$ whose objects are in bijection with the simple closed orbits of $\Phi$. In contrast with the Weinstein case, $\mathcal{W}_0$ is \emph{not homologically smooth}, as it is not finitely split-generated in a maximal way. We expect $\mathcal{W}_0$ to be a powerful new invariant of Anosov flows. This talk is partly based on joint work with Oleg Lazarev and Agustin Moreno.