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arXiv · 2409.02211

Multiplicity free covering of a graded manifold

Elizaveta Vishnyakova
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Abstract

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.

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Elizaveta Vishnyakova. 2025-05-09. Multiplicity free covering of a graded manifold. https://arxiv.org/abs/2409.02211

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