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Publication Date:
September 2009
ISSN:
1615-7168
DOI:
10.1515/ADVGEOM.2009.032

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Advances in Geometry

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

Christoph Müller1 / Christoph Wockel2

1Fachbereich Mathematik, Technische Universität Darmstadt, Schlossgartenstraße 7, 64289 Darmstadt, Germany. Email: mathematik@c-mueller.eu

2Fachbereich Mathematik, Technische Universität Darmstadt, Schlossgartenstraße 7, 64289 Darmstadt, Germany. Email: christoph@wockel.eu

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

Publication History:
Published Online:
2009-09-10

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

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