Higher categories of bordisms with geometric structures

Fuente: arXiv
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Autori principali: Grady, Daniel, Pavlov, Dmitri
Natura: Preprint
Pubblicazione: 2026
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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