Extended TQFTs via Generators and Relations I: The Extended Toric Code
| Autor: | Bruce Bartlett, Gerrit Goosen |
|---|---|
| Přispěvatelé: | 29845467 - Goosen, Gerrit |
| Rok vydání: | 2020 |
| Předmět: |
Quantum topology
Topological quantum field theory Toric code Applied Mathematics General Mathematics 010102 general mathematics Mathematics - Category Theory Geometric Topology (math.GT) 01 natural sciences 57R56 (Primary) 57M27 (Secondary) Algebra Mathematics - Geometric Topology String-net Mathematics - Quantum Algebra FOS: Mathematics Quantum Algebra (math.QA) Category Theory (math.CT) 0101 mathematics Mathematics |
| DOI: | 10.48550/arxiv.2001.08191 |
| 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: | OpenAIRE |
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