$(3-\epsilon)$-dimensional TQFTs from derived quantum group representations

Abstract: I will discuss joint work with Agustina Czenky. We introduce a $(3-\epsilon)$-dimensional TQFTs which is generated, in some sense, by the derived category of quantum group representations. This TQFT is valued in the $\infty$-category of dg vector spaces, and the value on a genus $g$ surface is a $g$-th iterate of the Hochschild cohomology for the aforementioned category. I will explain how this TQFT arises as a derived variant of the usual Reshetikhin–Turaev theory and, if time allows, I will discuss the possibility of introducing local systems into the theory. Our interest in local systems comes from proposed relationships with 4-dimensional non-topological QFT.

mathematical physicsalgebraic topologycategory theoryquantum algebra

Audience: researchers in the topic

Topological Quantum Field Theory Club (IST, Lisbon)

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