A split action associated with a compact transformation group
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Abstract:
We associate with an effective action of a compact connected Lie group as a pathwise connected space $X$ a split action of a quotient group $G/K$ on the quotient space $X/K$. One application of the main theorem states that if $X$ is a compact oriented manifold whose principal cohomology class is a cup product of one-dimensional classes then the action of $G$ on $X$ splits. We prove this in the differentiate case; the topological case has since been dealt with by Schultz.References
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Additional Information
- © Copyright 1981 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 83 (1981), 817-824
- MSC: Primary 57S05; Secondary 54H15
- DOI: https://doi.org/10.1090/S0002-9939-1981-0630061-4
- MathSciNet review: 630061