Two approaches to supermanifolds

Batchelor, Marjorie

doi:10.1090/S0002-9947-1980-0554332-9

Two approaches to supermanifolds
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Trans. Amer. Math. Soc. 258 (1980), 257-270 Request permission

Abstract:

The problem of supplying an analogue of a manifold whose sheaf of functions contains anticommuting elements has been approached in two ways. Either one extends the sheaf of functions formally, as in the category of graded manifolds [3], [8], or one mimicks the usual definition of a manifold, having replaced Euclidean space with a suitable product of the odd and even parts of an exterior algebra as in the category of supermanifolds [6]. This paper establishes the equivalence of the category of supermanifolds with the category of graded manifolds.

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