Volume 17, issue 2 (2017)

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On $\mathop{\mathrm{RO}}(G)$–graded equivariant “ordinary” cohomology where $G$ is a power of $\mathbb{Z}/2$

John Holler and Igor Kriz

Algebraic & Geometric Topology 17 (2017) 741–763
Abstract

We compute the complete $RO\left(G\right)$–graded coefficients of “ordinary” cohomology with coefficients in $ℤ∕2$ for $G={\left(ℤ∕2\right)}^{n}$. As an important intermediate step, we identify the ring of coefficients of the corresponding geometric fixed point spectrum, revealing some interesting algebra. This is a first computation of its kind for groups which are not cyclic $p$–groups.

Keywords
equivariant cohomology, geometric fixed points, isotropy separation
Primary: 55N91