TQFT for $\hat{Z}$ invariants

The $\hat{Z}$-invariants of three-manifolds introduced by Gukov, Pei, Putrov, and Vafa have influenced many areas of mathematics and physics. However, their TQFT structure is not yet fully understood. In this talk, I will present a framework for decorated Spin-TQFTs and construct one based on Atiyah–Segal-like axioms that computes the $\hat{Z}$-invariants. This TQFT framework provides a new perspective on the structural properties and gluing formulas for $\hat{Z}$-invariants.