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Transactions of the American Mathematical Society

Published by the American Mathematical Society, the Transactions of the American Mathematical Society (TRAN) is devoted to research articles of the highest quality in all areas of pure and applied mathematics.

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

The 2020 MCQ for Transactions of the American Mathematical Society is 1.43.

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Torus actions on a cohomology product of three odd spheres
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by Christopher Allday PDF
Trans. Amer. Math. Soc. 203 (1975), 343-358 Request permission

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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Additional Information
  • © Copyright 1975 American Mathematical Society
  • 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