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Journal of Lie Theory, Vol. 10, No. 2, pp. 359-373 (2000)
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Infinite dimensional manifold structures on principal bundles

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Maurice J. Dupré and James F. Glazebrook

Maurice Dupré

Department of Mathematics

Tulane University

New Orleans, LA 70118 USA

mdupre@mailhost.tcs.tulane.edu

and

James F. Glazebrook

Department of Mathematics

Eastern Illinois University

Charleston, IL 61920 USA

and

Department of Mathematics

University of Illinois

Urbana IL 61801 USA

glazebro@math.uiuc.edu

**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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