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Modular transformations of homological blocks for Seifert fibered homology $3$-spheres (2112.06210v2)
Published 12 Dec 2021 in math.GT, hep-th, math-ph, math.MP, and math.NT
Abstract: In this article, for any Seifert fibered integral homology 3-sphere, we give explicit modular transformation formulas of homological blocks introduced by Gukov-Pei-Putrov-Vafa. Moreover, based on the modular transformation formulas, we have explicit asymptotic expansion formulas for the Witten-Reshetikhin-Turaev invariants which give a new proof of a version by Andersen of the Witten asymptotic conjecture.