Topological Strings, D-Model, and Knot Contact Homology

Understand

We study the connection between topological strings and contact homology recently proposed in the context of knot invariants.

• In particular, we establish the proposed relation between the Gromov-Witten disk amplitudes of a Lagrangian associated to a knot and augmentations of its contact homology algebra.
• This also implies the equality between the Q-deformed A-polynomial and the augmentation polynomial of knot contact homology (in the irreducible case).
• We also generalize this relation to the case of links and to higher rank representations for knots.