Journal of Lie Theory, Vol. 10, No. 2, pp. 359-373 (2000)

Infinite dimensional manifold structures on principal bundles

Maurice J. Dupré and James F. Glazebrook

Maurice Dupré
Department of Mathematics
Tulane University
New Orleans, LA 70118 USA
James F. Glazebrook
Department of Mathematics
Eastern Illinois University
Charleston, IL 61920 USA
Department of Mathematics
University of Illinois
Urbana IL 61801 USA

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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