The theory of 𝐺^{∞}-supermanifolds

Boyer, Charles P.; Gitler, Samuel

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

The theory of $G\sp{\infty }$ -supermanifolds

Authors: Charles P. Boyer and Samuel Gitler
Journal: Trans. Amer. Math. Soc. 285 (1984), 241-267
MSC: Primary 58A50; Secondary 53C99, 58C50, 81G20, 83E50
DOI: https://doi.org/10.1090/S0002-9947-1984-0748840-9
MathSciNet review: 748840
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Abstract: A theory of supermanifolds is developed in which a supermanifold is an ordinary manifold associated with a certain integrable second order -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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