Witten-Reshetikhin-Turaev function for a knot in Seifert manifolds

Abstract

In this paper, for a Seifert loop (i.e., a knot in a Seifert three-manifold), first we give a family of an explicit function $\Phi (q;N)$ whose special values at roots of unity are identified with the Witten-Reshetikhin-Turaev invariants of the Seifert loop for the integral homology sphere. Second, we show that the function $\Phi (q;N)$ satisfies a $q$-difference equation whose classical limit coincides with a component of the character varieties of the Seifert loop. Third, we give an interpretation of the function $\Phi (q;N)$ from the view point of the resurgent analysis.

arXiv comment23 pages, 1 figure. References are added in v3

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Cited by in corpus (3)

• Resurgence in Lorentzian quantum cosmology: No-boundary saddles and resummation of quantum gravity corrections around tunneling saddle points
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• Witten-Reshetikhin-Turaev Invariants, Homological Blocks, and Quantum Modular Forms for Unimodular Plumbing H-Graphs