Infinitesimal characterization of homogeneous bundles
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- by Kirill Mackenzie PDF
- Proc. Amer. Math. Soc. 103 (1988), 1271-1277 Request permission
Abstract:
Consider a principal bundle $Q(B,H)$ on a base $B$ which is compact and has finite fundamental group. We give necessary and sufficient conditions, in terms of the Atiyah sequence of $Q(B,H)$, for $Q(B,H)$ to be locally isomorphic to a bundle of the form $G(G/S,S)$ for $G$ a Lie group and $S$ a closed subgroup of $G$. The proof involves the careful integration of certain infinitesimal actions of a Lie algebra on $Q,B$ and the universal cover of $B$.References
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Additional Information
- © Copyright 1988 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 103 (1988), 1271-1277
- MSC: Primary 55R20; Secondary 53C05, 53C10, 57R22
- DOI: https://doi.org/10.1090/S0002-9939-1988-0955021-1
- MathSciNet review: 955021