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Higher Categories and Topological Quantum Field Theories

QMAP Seminar

Speaker: Shawn Cui, Stanford
Location: 2112 MSB
Start time: Fri, Sep 29 2017, 1:30PM

We construct a Turaev-Viro type invariant of smooth closed oriented 4-manifolds out of a G-crossed braided spherical fusion category (G-BSFC) for G a finite group. The construction can be extended to obtain a (3+1)-dimensional topological quantum field theory (TQFT). The invariant generalizes several known ones in literature such as Yetter's invariant from homotopy 2-types and Crane-Yetter invariant. It remains to see if the invariant is sensitive to smooth structures. It is expected that the most general input to the construction of (3+1)-TQFTs is a spherical fusion 2-category. We show that a G-BSFC corresponds to a monoidal 2-category with certain extra structures, but these structures do not satisfy all the axioms of a spherical fusion 2-category given by M. Mackaay. Thus the question of what axioms properly define a spherical fusion 2-category is open.