The standard WDVV equations are PDEs in the potential function that generates Gromov-Witten invariants. These equations imply relations on the invariants, and sometimes allow computations thereof, as demonstrated by Kontsevich-Manin (1994). We prove analogous equations for open Gromov-Witten invariants that we defined in a previous work. For (ℂPn,ℝPn), the resulting relations allow the computation of all invariants. The formulation of the open WDVV requires a lift of the big quantum product to relative cohomology. Surprisingly, this brings us to use moduli spaces of disks with geodesic conditions. No prior knowledge of the subjects mentioned above will be assumed.
This is joint work with Jake Solomon.
This video is part of the Institute for Advanced Study‘s Symplectic geometry seminar.
