Multiplicity free covering of a graded manifold

2024/09/03 by Vishnyakova, Elizaveta · 1 citation
#Commutative Algebra (math.AC) #Differential Geometry (math.DG) #FOS: Mathematics #Symplectic Geometry (math.SG)

paper · doi:10.48550/arxiv.2409.02211

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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• Equivalence functors in graded supergeometry

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