The Resurgent Structure of Quantum Knot Invariants

  title={The Resurgent Structure of Quantum Knot Invariants},
  author={Stavros Garoufalidis and Jie Gu and Marcos Mari{\~n}o},
  journal={Communications in Mathematical Physics},
  pages={469 - 493}
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 to… Expand
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