#  Seminar, Shawn Cui (Virginia Tech), Four Dimensional Topological Quantum Field Theories from $G$-crossed Braided Categories 

 



####  calendar\_today Date and Time 

 **April 30, 2019** 

 03:00PM - 03:00PM EDT 

####  pin\_drop Location 

 **Jefferson 356**  



 

 



 

   ![Shawn Cui](/sites/g/files/omnuum6611/files/styles/hwp_1_1__360x360_scale/public/mathpicture/files/unnamed_02.jpg?itok=xRPbPT8Z) 

 

 **Title.** Four Dimensional Topological Quantum Field Theories from $G$-crossed Braided Categories

 **Abstract.** We construct a state-sum 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 of 4-manifolds generalizes several known invariants in literature such as the Crane-Yetter invariant from a ribbon fusion category and Yetter's invariant from homotopy 2-types. Furthermore, a cohomology class in $H^4(G,U(1))$ can be introduced to produce a different invariant, which reduces to the twisted Dijkgraaf-Witten theory in a special case. Very recently, Reutter and Douglas generalized the above construction to spherical fusion 2-categories, which is expected to produce the most general (3+1)-TQFTs of state-sum type.



 

 



 

 

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