Tangle addition and the knots-quivers correspondence

Stosic, Marko; Wedrich, Paul

doi:10.1112/jlms.12433

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Tangle addition and the knots-quivers correspondence

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Wedrich, Paul
Max Planck Institute for Mathematics, Max Planck Society;

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https://doi.org/10.1112/jlms.12433
(Publisher version)

https://doi.org/10.48550/arXiv.2004.10837
(Preprint)

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Citation

Stosic, M., & Wedrich, P. (2021). Tangle addition and the knots-quivers correspondence. Journal of the London Mathematical Society, 104(1), 341-361. doi:10.1112/jlms.12433.

Cite as: https://hdl.handle.net/21.11116/0000-0008-0E91-5

Abstract

We prove that the generating functions for the one row/column colored
HOMFLY-PT invariants of arborescent links are specializations of the generating
functions of the motivic Donaldson-Thomas invariants of appropriate quivers
that we naturally associate with these links. Our approach extends the
previously established tangles-quivers correspondence for rational tangles to
algebraic tangles by developing gluing formulas for HOMFLY-PT skein generating
functions under Conway's tangle addition. As a consequence, we prove the
conjectural links-quivers correspondence of
Kucharski-Reineke-Sto\v{s}i\'c-Sulkowski for all arborescent links.