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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.

References [Enhancements On Off] (What's this?)

  • [1] T. tom Dieck, Transformation groups and representation theory, Lecture Notes in Math., vol. 766, Springer-Verlag, Berlin and New York, 1979. MR 551743 (82c:57025)
  • [2] G. Segal, Equivariant stable homotopy theory, Proceedings ICM, Nice, 1970. MR 0423340 (54:11319)
  • [3 S] Waner and Y. Wu, The local structure of tangent $ G$-vector fields, Topology Appl. (to appear). MR 855452 (88c:55012)

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Article copyright: © Copyright 1987 American Mathematical Society

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