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Transactions of the American Mathematical Society

ISSN 1088-6850(online) ISSN 0002-9947(print)

 

 

Torus actions on a cohomology product of three odd spheres


Author: Christopher Allday
Journal: Trans. Amer. Math. Soc. 203 (1975), 343-358
MSC: Primary 57E25
DOI: https://doi.org/10.1090/S0002-9947-1975-0377953-3
MathSciNet review: 0377953
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Abstract: The main purpose of this paper is to describe how a torus group may act on a space, $ X$, whose rational cohomology ring is isomorphic to that of a product of three odd-dimensional spheres, in such a way that the fixed point set is nonempty, and $ X$ is not totally nonhomologous to zero in the associated $ X$-bundle, $ {X_T} \to {B_T}$. In the first section of the paper some general results on the cohomology theory of torus actions are established. In the second section the cohomology theory of the above type of action is described; and in the third section the results of the first two sections are used to prove a Golber formula for such actions, which, under certain conditions, bears an interesting interpretation in terms of rational homotopy.


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DOI: https://doi.org/10.1090/S0002-9947-1975-0377953-3
Keywords: Torus actions, equivariant cohomology, Golber formula
Article copyright: © Copyright 1975 American Mathematical Society