USC Topology Seminar: Partially wrapped contact Fukaya categories of 1-jet spaces

Hanming Liu, University of Oregon

Title: Partially wrapped contact Fukaya categories of 1-jet spaces

Abstract: Everyone loves Fukaya categories, which are categories of Lagrangians in symplectic manifolds. Naturally, a contact topologist would want to study contact Fukaya categories, which in analogy, would be categories of Legendrians in contact manifolds. Contact Fukaya categories is a rather unexplored topic at the moment. In this talk, I will introduce one incarnation of contact Fukaya categories: given a 1-jet space and a closed subset (called the stop), we define the partially wrapped contact Fukaya categories. It turns out that if the stop is nice enough, these categories are equivalent to certain microlocal sheaf categories. Since prior work shows that the "augmentations are sheaves" conjecture fails for certain Legendrians in the general 1-jet space setting, the partially wrapped contact Fukaya categories should be viewed as the correct generalization of the Floer-sheaf correspondence for Legendrians.