Differential graded manifolds of finite positive amplitude
Fuente:
arXiv
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| Autori principali: | , , |
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| Natura: | Preprint |
| Pubblicazione: |
2023
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| _version_ | 1866913226720018432 |
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| author | Behrend, Kai Liao, Hsuan-Yi Xu, Ping |
| author_facet | Behrend, Kai Liao, Hsuan-Yi Xu, Ping |
| contents | We prove that dg manifolds of finite positive amplitude, i.e. bundles of positively graded curved $L_\infty[1]$-algebras, form a category of fibrant objects. As a main step in the proof, we obtain a factorization theorem using path spaces. First we construct an infinite-dimensional factorization of a diagonal morphism using actual path spaces motivated by the AKSZ construction. Then we cut down to finite dimensions using the Fiorenza-Manetti method. The main ingredient in our method is the homotopy transfer theorem for curved $L_\infty[1]$-algebras. As an application, we study the derived intersections of manifolds. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2307_10242 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Differential graded manifolds of finite positive amplitude Behrend, Kai Liao, Hsuan-Yi Xu, Ping Differential Geometry High Energy Physics - Theory Algebraic Geometry Algebraic Topology Category Theory We prove that dg manifolds of finite positive amplitude, i.e. bundles of positively graded curved $L_\infty[1]$-algebras, form a category of fibrant objects. As a main step in the proof, we obtain a factorization theorem using path spaces. First we construct an infinite-dimensional factorization of a diagonal morphism using actual path spaces motivated by the AKSZ construction. Then we cut down to finite dimensions using the Fiorenza-Manetti method. The main ingredient in our method is the homotopy transfer theorem for curved $L_\infty[1]$-algebras. As an application, we study the derived intersections of manifolds. |
| title | Differential graded manifolds of finite positive amplitude |
| topic | Differential Geometry High Energy Physics - Theory Algebraic Geometry Algebraic Topology Category Theory |
| url | https://arxiv.org/abs/2307.10242 |