Skein modules and 4d TQFTs

Abstract: It is well-known that the quantum Chern–Simons theory (as formalized by Reshetikhin and Turaev) has a framing anomaly: to have a functorial dependence on cobordisms, they have to be equipped with an extra tangential structure besides the orientation. Following Walker and Freed–Teleman, one can view the anomaly of the Chern–Simons theory as an invertible 4d TQFT, the Crane–Yetter theory. While the Chern–Simons theory makes sense only when q, the quantum parameter, is a root of unity, the anomaly theory make sense for any q. I will describe the behavior of this 4d TQFT for generic q and, in particular, a description of its spaces of states on closed 3-manifolds. This is based on joint work with Sam Gunningham and David Jordan.

mathematical physicsalgebraic topologycategory theoryquantum algebra

Audience: researchers in the topic

Topological Quantum Field Theory Club (IST, Lisbon)

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