Northern California Symplectic Geometry Seminar: Open Gromov-Witten invariants and the HOMFLY skein relation

Seminar | February 5 | 4-5 p.m. | 891 Evans Hall

 Tobias Ekholm, Uppsala

 Department of Mathematics

Results of Witten and Ooguri-Vafa relate the HOMFLY polynomial of a link in the 3-sphere to the open topological string partition function of the Lagrangian conormal of the link, moved from the cotangent bundle of the 3-sphere to the resolved conifold. The mathematical counterpart of open topological string is open Gromov-Witten theory. We construct open Gromov-Witten invariants of conormal Lagrangians of links as counts of generalized holomorphic curves. We use the invariants to define a Gromov-Witten counterpart of the HOMFLY polynomial that we then show satisfies the skein relation. The talk reports on joint work in progress with Shende.