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

Hiroyuki Fuji; Kohei Iwaki; Hitoshi Murakami; Yuji Terashima

doi:10.1007/s00220-021-03953-y

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arXiv · 2007.15872

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

Hiroyuki Fuji·Kohei Iwaki·Hitoshi Murakami·Yuji Terashima

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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.

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BibTeX RIS

Hiroyuki Fuji, Kohei Iwaki, Hitoshi Murakami, Yuji Terashima. 2020-07-31. Witten-Reshetikhin-Turaev function for a knot in Seifert manifolds. https://doi.org/10.1007/s00220-021-03953-y

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