Defining extended TQFTs via handle attachments
Fuente:
arXiv
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| Format: | Preprint |
| Publié: |
2024
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| _version_ | 1866908757874704384 |
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| author | Haïoun, Benjamin |
| author_facet | Haïoun, Benjamin |
| contents | We give a finite presentation of the cobordism symmetric monoidal bicategory of (smooth, oriented) closed manifolds, cobordisms and cobordisms with corners as an extension of the bicategory of closed manifolds, cobordisms and diffeomorphisms. The generators are the standard handle attachments, and the relations are handle cancellations and invariance under reversing the orientation of the attaching spheres.
In other words, given a categorified TQFT and 2-morphisms associated to the standard handles satisfying our relations, we construct a once extended TQFT. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2412_14649 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Defining extended TQFTs via handle attachments Haïoun, Benjamin Geometric Topology Category Theory Quantum Algebra We give a finite presentation of the cobordism symmetric monoidal bicategory of (smooth, oriented) closed manifolds, cobordisms and cobordisms with corners as an extension of the bicategory of closed manifolds, cobordisms and diffeomorphisms. The generators are the standard handle attachments, and the relations are handle cancellations and invariance under reversing the orientation of the attaching spheres. In other words, given a categorified TQFT and 2-morphisms associated to the standard handles satisfying our relations, we construct a once extended TQFT. |
| title | Defining extended TQFTs via handle attachments |
| topic | Geometric Topology Category Theory Quantum Algebra |
| url | https://arxiv.org/abs/2412.14649 |