GP seminar: Open String Partition Function for Knot Complements

Abstract: Using the Ekholm–Shende formalism of the Ooguri–Vafa conjecture, we derive a flow-loop formula for the skein-valued partition function of A-model open topological strings with Lagrangian A-branes wrapping the complement of a fibered knot in the cotangent bundle of S^3 and in the resolved conifold. For torus knots, we show that the partition function localizes on two or three holomorphic annuli, and we obtain a corresponding generalized quiver structure.

Moreover, we relate our formula to the augmentation curve by determining a quantized augmentation polynomial that annihilates the partition function in the gl_1 skein, yielding another geometrically defined coordinate chart for the associated D-module.

This is based on the joint work with Tobias Ekholm and Pietro Longhi (arXiv: 2601.22922).

This is a seminar in the Centre of Geometry and Physics seminar series.