Infinite dimensional manifold structures on principal bundles

Abstract: Infinite dimensional fiber spaces arise naturally in the theory of representations of C$^*$-algebras. Often there are cases where one has to deal with more general notions of differentiability. In order to create a unified framework, we introduce the notion of a $\cal D$-space and a $\cal D$-group action in a given category $\cal D$ . Then we proceed to develop a general theory for studying the manifold structure of subsequent $\cal D$-orbit spaces and principal bundles which is applicable in infinite dimensions.

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