Abstract

Based on large N Chern-Simons/topological string duality, in a series of papers [37, 21, 19], J.M.F. Labastida, M. Mari˜no, H. Ooguri and C. Vafa conjectured certain remarkable new algebraic structure of link invariants and the existence of infinite series of new integer invariants. In this paper, we provide a proof of this conjecture. Moreover, we also show these new integer invariants vanish at large genera.