Skeins on Branes

Understand

We study 1-parameter families of holomorphic curves with Lagrangian boundary in Calabi-Yau 3-folds.

• We show that the expected codimension one phenomena can be organized to match the HOMFLYPT skein relations from quantum topology.
• It follows that counting holomorphic curves by the class of their boundaries in the skein module of the Lagrangian gives a deformation invariant result.
• This is a mathematically rigorous incarnation of Witten's assertion that boundaries of open topological strings create line defects in Chern-Simons theory.