Relative quantum product and open WDVV equations

Princeton/IAS Symplectic Geometry Seminar
Topic:Relative quantum product and open WDVV equations
Speaker:Sara Tukachinsky
Affiliation:University of Montreal
Date:Thursday, February 2
Time/Room:10:45am - 11:45am/S-101
Video Link:https://video.ias.edu/puias/2017/0202-SaraTukachinsky

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 ($\mathbb CP^n$ ,$\mathbb RP^n$), 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. This is joint work with Jake Solomon. No prior knowledge of the subjects mentioned above will be assumed.