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The Set of Balanced Orbits of Maps of S 1 and S 3 Actions
Proceedings of the American Mathematical Society
Suppose that the group G = S1 or G = S3 acts freely on a space X and on a representation space V for G. Let /: X -» V. The paper studies the size of the subset of X consisting of orbits over which the average of / is zero. The result can be viewed as an extension of the Borsuk-Ulam theorem. 2. The set of balanced points. (2.1) Definition. Let v be a G-space and let F be a finite-dimensional representation space of G. A map /: X -» V is said to be balanced at a point x G X if (Av/)x = 0. (Wedoi:10.2307/2045787 fatcat:dvwlu2pmujatxesp7bsda4bq7q