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

 

The set of balanced orbits of maps of $ S\sp 1$ and $ S\sp 3$ actions


Author: Jan Jaworowski
Journal: Proc. Amer. Math. Soc. 98 (1986), 158-162
MSC: Primary 57S10; Secondary 55M20, 55N25, 55R40
MathSciNet review: 848895
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Abstract: Suppose that the group $ G = {S^1}$ or $ G = {S^3}$ acts freely on a space $ X$ and on a representation space $ V$ for $ G$. Let $ f:X \to V$. The paper studies the size of the subset of $ X$ consisting of orbits over which the average of $ f$ is zero. The result can be viewed as an extension of the Borsuk-Ulam theorem.


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Additional Information

DOI: http://dx.doi.org/10.1090/S0002-9939-1986-0848895-4
PII: S 0002-9939(1986)0848895-4
Keywords: Average, equivariant map, equivariant cohomology, characteristic class, index
Article copyright: © Copyright 1986 American Mathematical Society