Extended TQFTs via generators and relations I: The extended toric code
Abstract
In his PhD thesis [G. Goosen, Oriented 123-tqfts via string-nets and state-sums, PhD thesis, Stellenbosch University, Stellenbosch (2018)], Goosen combined the string-net and the generators-and-relations formalisms for arbitrary once-extended 3-dimensional topological quantum field theories (TQFTs). In this paper, we work this out in detail for the simplest nontrivial 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
URI
http://hdl.handle.net/10394/36271https://www.worldscientific.com/doi/abs/10.1142/S0219199720500546
https://doi.org/10.1142/S0219199720500546