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

Christoph Müller 1  and Christoph Wockel 2
  • 1 Fachbereich Mathematik, Technische Universität Darmstadt, Schlossgartenstraße 7, 64289 Darmstadt, Germany. Email: mathematik@c-mueller.eu
  • 2 Fachbereich Mathematik, Technische Universität Darmstadt, Schlossgartenstraße 7, 64289 Darmstadt, Germany. Email: christoph@wockel.eu

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.

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Advances in Geometry is a mathematical journal which publishes original research articles of excellent quality in the area of geometry. Geometry is a field of long-standing tradition and eminent importance. The study of space and spatial patterns is a major mathematical activity, and geometric ideas and the geometric language permeate all of mathematics.

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