On the structure of étale fibrations of $L_\infty$-bundles
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arXiv
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| Main Authors: | , , |
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| Format: | Preprint |
| Published: |
2023
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| _version_ | 1866917297381179392 |
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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 an étale fibration between $L_\infty$-bundles admits local sections composed of several elementary morphisms of particularly simple and accessible type. As applications, we establish an inverse function theorem for $L_\infty$-bundles and provide an elementary proof that every weak equivalence of $L_\infty$-bundles induces a quasi-isomorphism of the differential graded algebras of global functions. Furthermore, we apply this inverse function theorem to show that the homotopy category of $L_\infty$-bundles admits a simple description in terms of homotopy classes of morphisms, when $L_\infty$-bundles are restricted to their germs around their classical loci. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2307_08179 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | On the structure of étale fibrations of $L_\infty$-bundles Behrend, Kai Liao, Hsuan-Yi Xu, Ping Differential Geometry Algebraic Geometry Algebraic Topology Category Theory We prove that an étale fibration between $L_\infty$-bundles admits local sections composed of several elementary morphisms of particularly simple and accessible type. As applications, we establish an inverse function theorem for $L_\infty$-bundles and provide an elementary proof that every weak equivalence of $L_\infty$-bundles induces a quasi-isomorphism of the differential graded algebras of global functions. Furthermore, we apply this inverse function theorem to show that the homotopy category of $L_\infty$-bundles admits a simple description in terms of homotopy classes of morphisms, when $L_\infty$-bundles are restricted to their germs around their classical loci. |
| title | On the structure of étale fibrations of $L_\infty$-bundles |
| topic | Differential Geometry Algebraic Geometry Algebraic Topology Category Theory |
| url | https://arxiv.org/abs/2307.08179 |