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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 $ 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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Additional Information

DOI: https://doi.org/10.1090/S0002-9947-1984-0748840-9
Keywords: Almost supermanifolds, exterior algebra, foliations, pseudogroups, supereuclidean space, supermanifolds
Article copyright: © Copyright 1984 American Mathematical Society

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