Extended TQFTs via Generators and Relations I: The Extended Toric Code

Autor:	Bartlett, Bruce, Goosen, Gerrit
Rok vydání:	2020
Předmět:	Mathematics - Quantum Algebra Mathematics - Category Theory Mathematics - Geometric Topology 57R56 (Primary) 57M27 (Secondary)
Druh dokumentu:	Working Paper
Popis:	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 $\mathbb{Z}/2\mathbb{Z}$-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. Comment: 28 pages. To appear in Communications in Contemporary Mathematics
Databáze:	arXiv
Externí odkaz:	http://arxiv.org/abs/2001.08191 Zobrazit plný text záznamu View this record from Arxiv