Moduli Spaces and Related Topics | "Counting" pseudo-holomorphic disks via loop space

Abstract：

Let M be a symplectic manifold and L be a Lagrangian submanifold. Celebrated work of Fukaya-Oh-Ohta-Ono constructs a filtered cyclic A-infinity algebra structure on the cochain (cohomology) group of L by studying moduli spaces of pseudo-holomorphic disks to (M,L) with boundary mark points. In this talk, I will explain how this A-infinity algebra lifts to the free loop space of L in a way compatible with the string topology of loop spaces, as well as some applications of this formalism.