TY - JOUR

T1 - Witten–Reshetikhin–Turaev Function for a Knot in Seifert Manifolds

AU - Fuji, Hiroyuki

AU - Iwaki, Kohei

AU - Murakami, Hitoshi

AU - Terashima, Yuji

N1 - Funding Information:
The authors are grateful to William Elbk Mistegrd, who kindly shear the new version of [] and informed us that the WRT function and are essentially the same q-series at least when . We also thank Kazuhiro Hikami, Masaya Kameyama, Nobushige Kurokawa, Serban Mihalache, Akihito Mori, Nobuo Sato and Sakie Suzuki for valuable comments and discussions. This work is partially supported by JSPS KAKENHI Grant Numbers JP16H03927, JP16H06337, JP17H06127, JP17K05239, JP17K05243, JP18K03281, JP20K03601, JP20K03931, JP20K14323. The authors would also express their deepest appreciation to Toshie Takata, who passed away on April 11th, 2020. She was one of the pioneers of Quantum Topology.
Publisher Copyright:
© 2021, The Author(s), under exclusive licence to Springer-Verlag GmbH, DE part of Springer Nature.
Copyright:
Copyright 2021 Elsevier B.V., All rights reserved.

PY - 2021

Y1 - 2021

N2 - 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.

AB - 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.

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U2 - 10.1007/s00220-021-03953-y

DO - 10.1007/s00220-021-03953-y

M3 - Article

AN - SCOPUS:85101879339

JO - Communications in Mathematical Physics

JF - Communications in Mathematical Physics

SN - 0010-3616

ER -