Multiplicity free covering of a graded manifold
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arXiv
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| Format: | Preprint |
| Published: |
2024
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| _version_ | 1866915278831484928 |
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| author | Vishnyakova, Elizaveta |
| author_facet | Vishnyakova, Elizaveta |
| contents | We define and study a multiplicity-free covering of a graded manifold. We compute its deck transformation group, which is isomorphic to the permutation group $S_n$. We show that it is not possible to construct a covering of a graded manifold in the category of $n$-fold vector bundles. As an application of our research, we give a new conceptual proof of the equivalence of the categories of graded manifolds and symmetric $n$-fold vector bundles. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2409_02211 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Multiplicity free covering of a graded manifold Vishnyakova, Elizaveta Differential Geometry Commutative Algebra Symplectic Geometry We define and study a multiplicity-free covering of a graded manifold. We compute its deck transformation group, which is isomorphic to the permutation group $S_n$. We show that it is not possible to construct a covering of a graded manifold in the category of $n$-fold vector bundles. As an application of our research, we give a new conceptual proof of the equivalence of the categories of graded manifolds and symmetric $n$-fold vector bundles. |
| title | Multiplicity free covering of a graded manifold |
| topic | Differential Geometry Commutative Algebra Symplectic Geometry |
| url | https://arxiv.org/abs/2409.02211 |