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Transactions of the American Mathematical Society

Published by the American Mathematical Society since 1900, Transactions of the American Mathematical Society is devoted to longer research articles 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 1.48.

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Localization of equivariant cohomology rings
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by J. Duflot PDF
Trans. Amer. Math. Soc. 284 (1984), 91-105 Request permission

Erratum: Trans. Amer. Math. Soc. 290 (1985), 857-858.

Abstract:

The main result of this paper is the "calculation" of the Borel equivariant cohomology ring ${H^{\ast } }(EG \times _G X,{\mathbf {Z}}/p{\mathbf {Z}})$ localized at one of its minimal prime ideals. In case $X$ is a point, the work of Quillen shows that the minimal primes ${\mathfrak {P}_A}$ are parameterized by the maximal elementary abelian $p$-subgroups $A$ of $G$ and the result is \[ {H^{\ast } }{(BG,{\mathbf {Z}}/p{\mathbf {Z}})_{{\mathfrak {P}_A}}} \cong {H^{\ast } }(B{C_G}(A),{\mathbf {Z}}/p{\mathbf {Z}})_{{\mathfrak {P}_A}}^{{W_G}(A)}\]. Here, ${C_G}(A)$ is the centralizer of $A$ in $G$, and ${W_G}(A) = {N_G}(A)/{C_G}(A)$, where ${N_G}(A)$ is the normalizer of $A$ in $G$. An example is included.
References
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Additional Information
  • © Copyright 1984 American Mathematical Society
  • Journal: Trans. Amer. Math. Soc. 284 (1984), 91-105
  • MSC: Primary 57S15; Secondary 20J06, 55N91
  • DOI: https://doi.org/10.1090/S0002-9947-1984-0742413-X
  • MathSciNet review: 742413