Infinitesimally natural principal bundles

Bas  Janssens

doi:10.3934/jgm.2016004

Article Contents

2016, Volume 8, Issue 2: 199-220. Doi: 10.3934/jgm.2016004

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Infinitesimally natural principal bundles

Bas Janssens^1,

1.
Universiteit Utrecht, Budapestlaan 6, 3584 CD Utrecht

Received: June 2015

Revised: April 2016

Published: June 2016

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Abstract

We extend the notion of a natural fibre bundle by requiring diffeomorphisms of the base to lift to automorphisms of the bundle only infinitesimally, i.e. at the level of the Lie algebra of vector fields. We classify the principal fibre bundles with this property. A version of the main result in this paper (theorem 4.4) can be found in Lecomte's work [12]. Our approach was developed independently, uses the language of Lie algebroids, and can be generalized in several directions.

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Mathematics Subject Classification: Primary: 53C27, 57R50, 22E65, 57R22.

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