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Rational links and DT invariants of quivers

MPS-Authors
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Stošić,  Marko
Max Planck Institute for Mathematics, Max Planck Society;

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

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Fulltext (public)

arXiv:1711.03333.pdf
(Preprint), 339KB

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Citation

Stošić, M., & Wedrich, P. (in press). Rational links and DT invariants of quivers. International Mathematics Research Notices, Published online 2019 - Print pending. doi:10.1093/imrn/rny289.


Cite as: http://hdl.handle.net/21.11116/0000-0006-9DD0-E
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-Sto\v{s}i\'c-Su{\l}kowski 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.