(Joint work with Chris Woodward) Consider a Lagrangian submanifold L̅ in a GIT quotient X̅=X//G. Besides the usual Fukaya A∞-algebra Fuk(L̅) defined by counting holomorphic disks, another version, called the quasimap Fukaya algebra FukK(L), is defined by counting holomorphic disks in X modulo group action. Motivated from the closed string quantum Kirwan map studied by Ziltener and Woodward, as well as the work of Fukaya-Oh-Ohta-Ono, Chan-Lau-Leung-Tseng, we construct an open string version of the quantum Kirwan map. This is an A∞-morphism from FukK(L) to a bulk deformation of Fuk(L̅). The deformation term is defined by counting affine vortices (point-like instantons) in the gauged sigma model, while the A∞-morphism is defined by counting point-like instantons with Lagrangian boundary condition.
This video is part of the Institute for Advanced Study‘s Symplectic geometry seminar.
