An Anosov flow Φ on a closed 3-manifold M gives rise to a non-Weinstein Liouville structure on V = [−1,1] × 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 homotopy class of Φ. We focus on a subcategory W0 of the wrapped Fukaya category of V whose objects are in bijection with the simple closed orbits of Φ. In contrast with the Weinstein case, W0 is not homologically smooth, as it is not finitely split-generated in a maximal way. We expect W0 to be a powerful new invariant of Anosov flows.
This talk is partly based on joint work with Oleg Lazarev and Agustin Moreno.
This video is part of the Institute for Advanced Study‘s Symplectic geometry seminar.
