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Most Downloaded Articles
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Equivalences of smooth and continuous principal bundles with infinite-dimensional structure group
1Fachbereich Mathematik, Technische Universität Darmstadt, Schlossgartenstraße 7, 64289 Darmstadt, Germany. Email: email@example.com
2Fachbereich Mathematik, Technische Universität Darmstadt, Schlossgartenstraße 7, 64289 Darmstadt, Germany. Email: firstname.lastname@example.org
Citation Information: Advances in Geometry. Volume 9, Issue 4, Pages 605–626, ISSN (Online) 1615-7168, ISSN (Print) 1615-715X, DOI: 10.1515/ADVGEOM.2009.032, September 2009
- Published Online:
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