# The Resurgent Structure of Quantum Knot Invariants

@article{Garoufalidis2020TheRS,
title={The Resurgent Structure of Quantum Knot Invariants},
author={S. Garoufalidis and Jie Gu and M. Mari{\~n}o},
journal={arXiv: High Energy Physics - Theory},
year={2020}
}
• Published 2020
• Physics, Mathematics
• arXiv: High Energy Physics - Theory
The asymptotic expansion of quantum knot invariants in complex Chern-Simons theory gives rise to factorially divergent formal power series. We conjecture that these series are resurgent functions whose Stokes automorphism is given by a pair of matrices of $q$-series with integer coefficients, which are determined explicitly by the fundamental solutions of a pair of linear $q$-difference equations. We further conjecture that for a hyperbolic knot, a distinguished entry of those matrices equals… Expand
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