The set of balanced orbits of maps of 𝑆¹ and 𝑆³ actions

Jaworowski, Jan

doi:10.1090/S0002-9939-1986-0848895-4

The set of balanced orbits of maps of $S^ 1$ and $S^ 3$ actions
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Proc. Amer. Math. Soc. 98 (1986), 158-162 Request permission

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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