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\(\Lambda\)-supermanifolds and fiber bundles. (English. Russian original) Zbl 0533.58005

Sov. Math., Dokl. 27, 350-353 (1983); translation from Dokl. Akad. Nauk SSSR 269, 524-527 (1983).
By analogy with the real and complex cases, the author introduces the superspaces and supermanifolds over a commutative Banach superalgebra \((=\) a graded commutative Banach algebra) \(\Lambda\). First he studies the foundations of the corresponding differential calculus including the inverse function theorem and a theorem on existence of solutions of ordinary differential equations. Then he deduces the basic facts from the theory of connections on a principal fiber \(\Lambda\)-superbundle.

MSC:

58B20 Riemannian, Finsler and other geometric structures on infinite-dimensional manifolds
53C05 Connections (general theory)