Resurgence analysis of quantum invariants of Seifert fibered homology spheres

For a Seifert fibered homology sphere X we show that the q-series invariant Zˆ0(X; q) introduced by Gukov-Pei-Putrov-Vafa, is a resummation of the Ohtsuki series Z0(X). We show that for every even k ∈ N there exists a full asymptotic expansion of Zˆ0(X; q) for q tending to e 2πi/k, and in particular that the limit Zˆ0(X; e 2πi/k) exists and is equal to the WRT quantum invariant τk(X). We show that the poles of the Borel transform of Z0(X) coincide with the classical complex Chern-Simons values, which we further show classifies the corresponding components of the moduli space of flat SL(2, C)-connections.