Topological recursion for the conifold transition of a torus knot

Abstract

In this paper we prove a mirror symmetry conjecture based on the work of Brini et al. (Ann Henri Poincaŕe 13(8):1873–1910, 2012) and Diaconescu et al. (Commun Math Phys 319(3):813–863, 2013). This conjecture relates open Gromov–Witten invariants of the conifold transition of a torus knot to the topological recursion on the B-model spectral curve.