2020/01/22 by Bartlett, Bruce, Goosen, Gerrit
#57R56 (Primary) 57M27 (Secondary) #Category Theory (math.CT) #FOS: Mathematics #Geometric Topology (math.GT) #Quantum Algebra (math.QA)
paper · doi:10.48550/arxiv.2001.08191
In his PhD thesis, Goosen combined the string-net and the generators-and-relations formalisms for arbitrary once-extended 3-dimensional TQFTs. In this paper we work this out in detail for the simplest non-trivial example, where the underlying spherical fusion category is the category of ℤ/2ℤ-graded vector spaces. This allows us to give an elementary string-net description of the linear maps associated to 3-dimensional bordisms. The string-net formalism also simplifies the description of the mapping class group action in the resulting TQFT. We conclude the paper by performing some example calculations from this viewpoint.