The theory of 𝐺^{∞}-supermanifolds

Boyer, Charles P.; Gitler, Samuel

doi:10.1090/S0002-9947-1984-0748840-9

The theory of $G^{\infty }$-supermanifolds
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by Charles P. Boyer and Samuel Gitler PDF

Trans. Amer. Math. Soc. 285 (1984), 241-267 Request permission

Abstract:

A theory of supermanifolds is developed in which a supermanifold is an ordinary manifold associated with a certain integrable second order $G$-structure. A structure theorem is proved showing that every ${G^\infty }$-supermanifold has a complete distributive lattice of foliations with flat affine leaves. Furthermore, an existence and uniqueness theorem for local flows of ${G^\infty }$ vector fields is proved.

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