Equivalences of Smooth and Continuous Principal Bundles with Infinite-Dimensional Structure Group

Abstract

Let K be a a Lie group, modeled on a locally convex space, and M a finite-dimensional paracompact manifold with corners. We show that each continuous principal K-bundle over M is continuously equivalent to a smooth one and that two smooth principal K-bundles over M which are continuously equivalent are also smoothly equivalent. In the concluding section, we relate our results to neighboring topics.

18 pages, final version

References in corpus (2)

• On a generalized Connes-Hochschild-Kostant-Rosenberg theorem
• Obstruction classes of crossed modules of Lie algebroids and Lie groupoids linked to existence of principal bundles

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