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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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1615-7168
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Volume 9, Issue 4

Issues

Equivalences of smooth and continuous principal bundles with infinite-dimensional structure group

Christoph Müller
  • Fachbereich Mathematik, Technische Universität Darmstadt, Schlossgartenstraße 7, 64289 Darmstadt, Germany. Email:
  • Other articles by this author:
  • De Gruyter OnlineGoogle Scholar
/ Christoph Wockel
  • Fachbereich Mathematik, Technische Universität Darmstadt, Schlossgartenstraße 7, 64289 Darmstadt, Germany. Email:
  • Other articles by this author:
  • De Gruyter OnlineGoogle Scholar
Published Online: 2009-09-10 | DOI: https://doi.org/10.1515/ADVGEOM.2009.032

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

About the article

Published Online: 2009-09-10

Published in Print: 2009-10-01


Citation Information: Advances in Geometry, Volume 9, Issue 4, Pages 605–626, ISSN (Online) 1615-7168, ISSN (Print) 1615-715X, DOI: https://doi.org/10.1515/ADVGEOM.2009.032.

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[1]
Thomas Nikolaus and Konrad Waldorf
Pacific Journal of Mathematics, 2013, Volume 264, Number 2, Page 355
[2]
Christoph Wockel
Forum Mathematicum, 2011, Volume 23, Number 3

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