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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 fixed-point theorem for $ p$-group actions


Author: Stefan Jackowski
Journal: Proc. Amer. Math. Soc. 102 (1988), 205-208
MSC: Primary 57S17,; Secondary 55P91
MathSciNet review: 915745
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Abstract: We prove Sullivan's fixed-point conjecture for fixed-point-free actions of compact Lie groups which are extensions of a $ p$-group by a torus. Moreover, we show that for a finite $ p$-group $ G$ and a compact or finitely dimensional paracompact $ G$-space $ X$ the fixed point set $ {X^G}$ is nonempty iff the induced homomorphism of zero-dimensional stable cohomotopy groups $ {\pi ^0}\left( {BG} \right) \to {\pi ^0}\left( {EG{ \times _G}X} \right)$ is injective.


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DOI: http://dx.doi.org/10.1090/S0002-9939-1988-0915745-9
PII: S 0002-9939(1988)0915745-9
Keywords: $ p$-group, fixed points, equivariant maps, sections, stable cohomotopy, the Sullivan conjecture, the Segal conjecture
Article copyright: © Copyright 1988 American Mathematical Society