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arXiv · 1708.06009

The $\mathbb{Z}/p$ ordinary cohomology of $B_G U(1)$

Steven R. Costenoble
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Abstract

With $G = \mathbb{Z}/p$, $p$ prime, we calculate the ordinary $G$-cohomology (with Burnside ring coefficients) of $\mathbb{C}P_G^\infty = B_G U(1)$, the complex projective space, a model for the classifying space for $G$-equivariant complex line bundles. The $RO(G)$-graded ordinary cohomology was calculated by Gaunce Lewis, but here we extend to a larger grading in order to capture a more natural set of generators, including the Euler class of the canonical bundle, as well as a significantly simpler set of relations.

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Steven R. Costenoble. 2017-08-20. The $\mathbb{Z}/p$ ordinary cohomology of $B_G U(1)$. https://arxiv.org/abs/1708.06009

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