A degree formula for equivariant cohomology

Lynn, Rebecca

doi:10.1090/S0002-9947-2013-05828-X

A degree formula for equivariant cohomology
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Trans. Amer. Math. Soc. 366 (2014), 309-339 Request permission

Abstract:

The primary theorem of this paper concerns the Poincaré (Hilbert) series for the cohomology ring of a finite group $G$ with coefficients in a prime field of characteristic $p$. This theorem is proved using the ideas of equivariant cohomology whereby one considers more generally the cohomology ring of the Borel construction $H^*(EG \times _G X)$, where $X$ is a manifold on which $G$ acts. This work results in a formula that computes the “degree” of the Poincaré series in terms of corresponding degrees of certain subgroups of the group $G$. In this paper, we discuss the theorem and the method of proof.

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