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Proceedings of the American Mathematical Society

ISSN 1088-6826(online) ISSN 0002-9939(print)

 
 

 

A note on the Borel formula


Author: Ronald M. Dotzel
Journal: Proc. Amer. Math. Soc. 78 (1980), 585-589
MSC: Primary 55M35; Secondary 57S17
DOI: https://doi.org/10.1090/S0002-9939-1980-0556637-X
MathSciNet review: 556637
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Abstract: A new proof of the Borel formula is obtained for $ G = {({Z_p})^r}$ actions on spaces X having $ {H_i}(X;{Z_p}) = 0,i \ne n$ (some n) and $ {H_n}(X;{Z_p}) = {Z_p} \oplus $ Free $ {Z_p}G$ module. Each $ {X^H}$ must be a $ {Z_p}$-homology $ n(H)$-sphere and then $ n - n(G) = \Sigma (n(H) - (G))$, sum running over corank 1 subgroups. A discussion of examples follows.


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DOI: https://doi.org/10.1090/S0002-9939-1980-0556637-X
Article copyright: © Copyright 1980 American Mathematical Society