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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

A split action associated with a compact transformation group


Author: Sol Schwartzman
Journal: Proc. Amer. Math. Soc. 83 (1981), 817-824
MSC: Primary 57S05; Secondary 54H15
MathSciNet review: 630061
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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.


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Additional Information

DOI: http://dx.doi.org/10.1090/S0002-9939-1981-0630061-4
PII: S 0002-9939(1981)0630061-4
Keywords: Equivariant map, split action
Article copyright: © Copyright 1981 American Mathematical Society