Modular Transformations of Homological Blocks for Seifert Fibered Homology 3-Spheres

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.