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Abstract
Let K be 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.
Key words.: Infinite-dimensional Lie groups; manifolds with corners; continuous principal bundles; smooth principal bundles; equivalences of continuous and smooth principal bundles; smoothing of continuous principal bundles; smoothing of continuous bundle equivalences; non-abelian Čech cohomology; twisted K-theory
Published Online: 2009-09-10
Published in Print: 2009-October
© de Gruyter 2009
