The Resurgent Structure of Quantum Knot Invariants

  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},
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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