Multiplicity free covering of a graded manifold

Elizaveta Vishnyakova

Multiplicity free covering of a graded manifold

Differential Geometry 2025-05-12 v3 Commutative Algebra Symplectic Geometry

Authors: Elizaveta Vishnyakova

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.

Keywords

graded manifold covering space deck transformation permutation group symmetric vector bundle

Cite

@article{arxiv.2409.02211,
  title  = {Multiplicity free covering of a graded manifold},
  author = {Elizaveta Vishnyakova},
  journal= {arXiv preprint arXiv:2409.02211},
  year   = {2025}
}

Comments

20 pages. Proposition 32 is corrected. Main results are unchanged. The text of the paper is reworked and simplified

Multiplicity free covering of a graded manifold

Abstract

Keywords

Cite

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