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The set of balanced points with respect to $ S\sp 1$ and $ S\sp 3$ actions of maps into Banach space

Author: Neža Mramor-Kosta
Journal: Proc. Amer. Math. Soc. 102 (1988), 723-727
MSC: Primary 55N91; Secondary 47H99
MathSciNet review: 929010
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Abstract: Let $ G$ be the group of units in the field $ F$, which is either $ R$, $ C$ or $ H$, let $ X$ be a free $ G$-space, and let $ f$ be a map from $ X$ to a Banach space $ E$ over $ F$. In this paper we give an estimate for the size of the subset of $ X$ consisting of points at which the average of $ f$ is equal to zero. The result represents an extension of the Borsuk-Ulam-Yang theorem.

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Keywords: Average, equivariant map, compact map, characteristic class, index, coindex of equivariant map
Article copyright: © Copyright 1988 American Mathematical Society

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