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Transactions of the American Mathematical Society
Transactions of the American Mathematical Society
ISSN 1088-6850(online) ISSN 0002-9947(print)

$ {\bf Z}/p{\bf Z}$ actions on $ (S\sp n)\sp k$


Author: Alejandro Adem
Journal: Trans. Amer. Math. Soc. 300 (1987), 791-809
MSC: Primary 57S17; Secondary 55R91, 57S25
MathSciNet review: 876479
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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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DOI: http://dx.doi.org/10.1090/S0002-9947-1987-0876479-6
PII: S 0002-9947(1987)0876479-6
Article copyright: © Copyright 1987 American Mathematical Society