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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 note on the existence of $ G$-maps between spheres


Author: Stefan Waner
Journal: Proc. Amer. Math. Soc. 99 (1987), 179-181
MSC: Primary 57S17; Secondary 55P91
MathSciNet review: 866449
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Abstract: Let $ G$ be a finite group, and let $ V$ and $ W$ be finite-dimensional real orthogonal $ G$-modules with $ V \supset W$, and with unit spheres $ S(V)$ and $ S(W)$ respectively. The purpose of this note is to give necessary sufficient conditions for the existence of a $ G$-map $ J:S(V) \to S(W)$ in terms of the Burnside ring of $ G$ and its relationship with $ V$ and $ W$. Note that if $ W$ has a nonzero fixed point, such a $ G$-map always exists, so for nontriviality, we assume this not the case.


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DOI: http://dx.doi.org/10.1090/S0002-9939-1987-0866449-1
PII: S 0002-9939(1987)0866449-1
Article copyright: © Copyright 1987 American Mathematical Society