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Infinite dimensional manifold structures on principal bundles. (English) Zbl 0964.58004

A categorical generalization of infinite dimensional manifolds on principal bundles is introduced. It generalizes both notions of differentiability and infinite dimensional fiber spaces arising in the theory of representations of \(C^*\)-algebras.
Several statements are proved that are such generalizations of structures of \(C^k\)-Banach manifolds and fibers on them. Applications to the Banach Lie group smooth actions on manifolds are considered. In addition, principal bundles on Banach Lie groups are discussed.

MSC:

58B25 Group structures and generalizations on infinite-dimensional manifolds
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