Stosic, MarkoWedrich, Paul2023-03-071073-7928http://hdl.handle.net/1885/286672We 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.M. S. was supported by the ERC Starting Grant [335739] “Quantum fields and knot homologies” funded by the European Research Council under the European Union’s Seventh Framework Programme, and by the Ministry of Education, Science, and Technological Development of the Republic of Serbia [174012]. P. W. was supported by the Leverhulme Trust [RP2013-K-017]application/pdfen-AU© 2018 The authors202110.1093/imrn/rny2892021-12-26