In this paper, for a Seifert loop (i.e., a knot in a Seifert three-manifold), first we give a family of explicit functions Φ (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 Φ (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 Φ (q; N) from the view point of the resurgent analysis.
ASJC Scopus subject areas
- Statistical and Nonlinear Physics
- Mathematical Physics