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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

Cohomology ring of the orbit space of certain free $ Z\sb p$-actions


Authors: Ronald M. Dotzel and Tej B. Singh
Journal: Proc. Amer. Math. Soc. 123 (1995), 3581-3585
MSC: Primary 57S17; Secondary 55R20
MathSciNet review: 1285986
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Abstract: In this paper, we consider actions of $ G = {Z_p}$ (with p an odd prime) on spaces X which are of cohomology type (0, 0) (i.e., have the $ \bmod$-$ p$ cohomology of the one-point union of an n-sphere, a 2n-sphere and a a 3n-sphere, n odd). If X is not totally non-homologous to zero in $ {X_G}$ we determine the fixed set, give examples of all possibilities for the fixed set and compute the cohomology ring structure of the orbit space in the case where G acts freely. In [4], we considered fixed sets for related spaces, when X is totally non-homologous to zero in $ {X_G}$.


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DOI: http://dx.doi.org/10.1090/S0002-9939-1995-1285986-6
PII: S 0002-9939(1995)1285986-6
Article copyright: © Copyright 1995 American Mathematical Society