Advances in Geometry
Managing Editor: Grundhöfer, Theo / Joswig, Michael
Editorial Board: Bannai, Eiichi / Coskun, Izzet / Duzaar, Frank / Eberlein, Patrick / Gentili, Graziano / Henk, Martin / Kantor, William M. / Korchmaros, Gabor / Kreuzer, Alexander / Lagarias, Jeffrey C. / Leistner, Thomas / Löwen, Rainer / Ono, Kaoru / Pasini, Antonio / Ratcliffe, John G. / Scharlau, Rudolf / Scheiderer, Claus / Van Maldeghem, Hendrik / Weintraub, Steven H. / Weiss, Richard
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IMPACT FACTOR 2016: 0.552
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Source Normalized Impact per Paper (SNIP) 2016: 1.021
Mathematical Citation Quotient (MCQ) 2016: 0.45
Equivalences of smooth and continuous principal bundles with infinite-dimensional structure group
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
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