Higher categories of bordisms with geometric structures
Fuente:
arXiv
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| Autori principali: | , |
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| Natura: | Preprint |
| Pubblicazione: |
2026
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| _version_ | 1866910190978203648 |
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| author | Grady, Daniel Pavlov, Dmitri |
| author_facet | Grady, Daniel Pavlov, Dmitri |
| contents | We introduce a system of axioms that uniquely defines an (infinity,d)-category of bordisms equipped with geometric data. The underlying manifolds of these bordisms may be smooth, complex, super, or formal smooth manifolds, as well as any class of manifolds satisfying conditions specified in this paper. We develop a general notion of a field on a manifold, encompassing structures such as Riemannian metrics, principal bundles with connection, conformal structures, and traditional tangential structures. Using this framework, we construct a symmetric monoidal (infinity,d)-category of bordisms with prescribed underlying manifolds and fields, and prove that it satisfies our axioms. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2605_03453 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Higher categories of bordisms with geometric structures Grady, Daniel Pavlov, Dmitri Algebraic Topology Mathematical Physics Quantum Algebra 57R56 (Primary) 81T45, 57R65, 57R15, 18N65 (Secondary) We introduce a system of axioms that uniquely defines an (infinity,d)-category of bordisms equipped with geometric data. The underlying manifolds of these bordisms may be smooth, complex, super, or formal smooth manifolds, as well as any class of manifolds satisfying conditions specified in this paper. We develop a general notion of a field on a manifold, encompassing structures such as Riemannian metrics, principal bundles with connection, conformal structures, and traditional tangential structures. Using this framework, we construct a symmetric monoidal (infinity,d)-category of bordisms with prescribed underlying manifolds and fields, and prove that it satisfies our axioms. |
| title | Higher categories of bordisms with geometric structures |
| topic | Algebraic Topology Mathematical Physics Quantum Algebra 57R56 (Primary) 81T45, 57R65, 57R15, 18N65 (Secondary) |
| url | https://arxiv.org/abs/2605.03453 |