Higher Structure Conferences Ekholm

Knot contact homology, topological strings and Chern-Simons theory

Abstract: We discuss the relation between the augmentation polynomial of knot contact homology and topological string theory in the resolved conifold. In essence, this gives two dual ways of computing the topological string at the disk level, through knot contact homology and through asymptotic of the coloured HOMFLY. The corresponding result at arbitrary genus relates the recursion relation for the HOMFLY to a version of symplectic field theory for the conormal of a knot, we discuss initial progress in this direction.