Rational Links and DT Invariants of Quivers

Abstract

We prove that the generating functions for the colored HOMFLY-PT polynomials of rational links are specializations of the generating functions of the motivic Donaldson-Thomas invariants of appropriate quivers that we naturally associate with these links. This shows that the conjectural links-quivers correspondence of Kucharski-Reineke-Stosic-Sulkowski as well as the LMOV conjecture holds for all rational links. Along the way, we extend the links-quivers correspondence to tangles and, thus, explore elements of a skein theory for motivic Donaldson-Thomas invariants. Show more