3d TQFTs and 3-manifold invariants
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arXiv
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| Autori principali: | , |
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| Natura: | Preprint |
| Pubblicazione: |
2024
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| _version_ | 1866909077276196864 |
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| author | Sozer, Kursat Virelizier, Alexis |
| author_facet | Sozer, Kursat Virelizier, Alexis |
| contents | This is an invited contribution to the 2nd edition of the Encyclopedia of Mathematical Physics. We give an overview of 3-dimensional topological quantum field theories (TQFTs) and the corresponding quantum invariants of 3-manifolds. We recall the main algebraic concepts and constructions, such as modular and spherical fusion categories, the Witten-Reshetikhin-Turaev and Turaev-Viro theories, and the relation between these two TQFTs. We also briefly discuss generalizations of these constructions by providing a (non-exhaustive) review of some recent works on 3-dimensional extended TQFTs, defect TQFTs, homotopy QFTs, and non-semisimple TQFTs. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2401_10587 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | 3d TQFTs and 3-manifold invariants Sozer, Kursat Virelizier, Alexis Geometric Topology Quantum Algebra 18M20, 57K31, 57K16 This is an invited contribution to the 2nd edition of the Encyclopedia of Mathematical Physics. We give an overview of 3-dimensional topological quantum field theories (TQFTs) and the corresponding quantum invariants of 3-manifolds. We recall the main algebraic concepts and constructions, such as modular and spherical fusion categories, the Witten-Reshetikhin-Turaev and Turaev-Viro theories, and the relation between these two TQFTs. We also briefly discuss generalizations of these constructions by providing a (non-exhaustive) review of some recent works on 3-dimensional extended TQFTs, defect TQFTs, homotopy QFTs, and non-semisimple TQFTs. |
| title | 3d TQFTs and 3-manifold invariants |
| topic | Geometric Topology Quantum Algebra 18M20, 57K31, 57K16 |
| url | https://arxiv.org/abs/2401.10587 |