Back to Search
Start Over
Extended TQFTs via Generators and Relations I: The Extended Toric Code
- Publication Year :
- 2020
- Publisher :
- arXiv, 2020.
-
Abstract
- 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.<br />Comment: 28 pages. To appear in Communications in Contemporary Mathematics
- Subjects :
- 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
Subjects
Details
- Database :
- OpenAIRE
- Accession number :
- edsair.doi.dedup.....0804901539c355566335719995855ac6
- Full Text :
- https://doi.org/10.48550/arxiv.2001.08191