The Rabinowitz Fukaya category and applications

Abstract: The goal of the talk is to introduce the Rabinowitz (wrapped) Fukaya category, as an open-string analogue of Rabinowitz Floer homology of (the boundary at infinity of) a Liouville manifold, which is a categorical invariant of exact cylindrical Lagrangians whose cohomology morphisms measure the failure of wrapped Floer cohomology to satisfy Poincare duality. The main result, answering a conjecture of Abouzaid, relates this category to the usual wrapped Fukaya category by a canonical algebraic formula, in terms of the categorical formal punctured neighborhood of infinity introduced by Efimov. As an application, we shall see a few new computations in Floer theory via homological mirror symmetry. In addition, we are going to explore the open-closed string relationship and derive structural and computational results in both Rabinowitz Floer homology and symplectic cohomology. This is based on joint work with Sheel Ganatra and Sara Venkatesh.

mathematical physicsalgebraic geometrysymplectic geometry

Audience: researchers in the topic

IBS-CGP weekly zoom seminar

Series comments: Registration is required at cgp.ibs.re.kr/activities/talkregistration