Modular transformations of homological blocks for Seifert fibered homology $3$-spheres

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.

arXiv comment22 pages, 1 figure, We have added Proposition 3.14 and corrected minor mistakes in the arguments in Section 5