2022/12/19 by Elizaveta Vishnyakova, Vishnyakova, Elizaveta
Mathematics · Medicine · #Algebraic structures and combinatorial models #Complex Variables (math.CV) #Differential Geometry (math.DG) #FOS: Mathematics #FOS: Physical sciences #Homotopy and Cohomology in Algebraic Topology #Mathematical Physics (math-ph) #Ophthalmology and Eye Disorders
paper · pdf · doi:10.48550/arxiv.2212.09558
openalex publication_date 2022/12/19 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We introduce and investigate the notion of a \mathbb Z-graded covering for a supermanifold. More precisely, Donagi and Witten suggested a construction of the first obstruction class for splitting of a supermanifold via differential operators. We prove that an infinite prolongation of this construction satisfies some universal properties and can be seen as a covering of a supermanifold in the category of graded manifolds.