Infinitesimal characterization of homogeneous bundles

Author:
Kirill Mackenzie

Journal:
Proc. Amer. Math. Soc. **103** (1988), 1271-1277

MSC:
Primary 55R20; Secondary 53C05, 53C10, 57R22

MathSciNet review:
955021

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Abstract: Consider a principal bundle on a base which is compact and has finite fundamental group. We give necessary and sufficient conditions, in terms of the Atiyah sequence of , for to be locally isomorphic to a bundle of the form for a Lie group and a closed subgroup of . The proof involves the careful integration of certain infinitesimal actions of a Lie algebra on and the universal cover of .

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DOI:
https://doi.org/10.1090/S0002-9939-1988-0955021-1

Article copyright:
© Copyright 1988
American Mathematical Society