Witten–Reshetikhin–Turaev Function for a Knot in Seifert Manifolds

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...

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Bibliographic Details
Published in:Communications in mathematical physics 2021-08, Vol.386 (1), p.225-251
Main Authors: Fuji, Hiroyuki, Iwaki, Kohei, Murakami, Hitoshi, Terashima, Yuji
Format: Article
Language:English
Subjects:
Classical and Quantum Gravitation
Complex Systems
Difference equations
Homology
Knots
Manifolds
Mathematical and Computational Physics
Mathematical Physics
Physics
Physics and Astronomy
Quantum Physics
Relativity Theory
Theoretical
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Summary: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.
ISSN:0010-3616
1432-0916
DOI:10.1007/s00220-021-03953-y