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$\hat{Z}$-TQFT, Surgery Formulas, and New Algebras
The $\hat{Z}$ invariants of three-manifolds introduced by Gukov-Pei-Putrov-Vafa have influenced many areas of mathematics and physics. However, their TQFT structure remains poorly understood. In this work, we develop a framework of decorated $\mathrm{Spin}$-TQFTs and construct one based on Atiyah-Se
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