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-Stošić-Sułkowski as well as the LMOV conjecture hold for 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.

28 pages, page numbers differ from published version

References in corpus (2)

• Knots-quivers correspondence
• BPS states, knots and quivers

Cited by in corpus (5)

• Branches, quivers, and ideals for knot complements
• Branes, quivers and wave-functions
• Tangle addition and the knots-quivers correspondence
• Quiver diagonalization and open BPS states
• Permutohedra for knots and quivers