$\hat{I}”$ Invariants of Plumbed Manifolds

Shimal Harichurn, András Némethi, Josef Svoboda

We study the minimal $q$-exponent $\hat{I}”$ in the BPS $q$-series $\hat{Z}$ of negative definite plumbed 3-manifolds equipped with a spin${}^{\mathrm{c}}$-structure. We express $\hat{I}”$ of Sei…