We explain how counting holomorphic curves with Lagrangian boundary conditions in a 6-dimensional symplectic Calabi-Yau manifolds by the values of their boundary links in the HOMFLYPT skein module of the Lagrangian resolves wall-crossing problems for invariance of open Gromov-Witten invariants. Combined with SFT stretching this leads both to a proof of the Gopakumar-Vafa conjecture, that relates the colored HOMFLYPT polynomials of a knot in the 3-sphere with open curve counts in the resolved conifold. The talk reports on joint work with Vivek Shende.
Skein valued curve counting
23.01.2024 09:45 - 11:15
Organiser:
A. Keating, B. Szendroi, V. Vertesi
Location: