𝑍/𝑝𝑍 actions on (𝑆ⁿ)^{𝑘}

Adem, Alejandro

doi:10.1090/S0002-9947-1987-0876479-6

$\textbf {Z}/p\textbf {Z}$ actions on $(S^ n)^ k$
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by Alejandro Adem PDF

Trans. Amer. Math. Soc. 300 (1987), 791-809 Request permission

Abstract:

Let ${\mathbf {Z}}/p$ act on a finitistic space $X$ with integral cohomology isomorphic to that of ${({S^n})^k}$ as a ring. We show a direct relationship between the ${\mathbf {Z}}/p$-module structure of ${H^n}(X;{\mathbf {Z}})$ and the nature of the fixed-point set. In particular, we obtain a significant restriction on ${H^n}(X;{\mathbf {Z}})$ for free actions.

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