Dupré, Maurice J.; Glazebrook, James F. Infinite dimensional manifold structures on principal bundles. (English) Zbl 0964.58004 J. Lie Theory 10, No. 2, 359-373 (2000). 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. Reviewer: Sergey Lüdkovsky (Moskva) Cited in 3 Documents MSC: 58B25 Group structures and generalizations on infinite-dimensional manifolds Keywords:categorical generalization; principal bundles; Banach Lie groups PDFBibTeX XMLCite \textit{M. J. Dupré} and \textit{J. F. Glazebrook}, J. Lie Theory 10, No. 2, 359--373 (2000; Zbl 0964.58004) Full Text: EuDML