The ℤ/p ordinary cohomology of B_G U(1)

2017/08/20 by Steven R. Costenoble, Costenoble, Steven R.
Mathematics · #55N91 55R91 (Secondary) #55R40 (Primary) #Algebraic Geometry and Number Theory #Algebraic Topology (math.AT) #Algebraic structures and combinatorial models #FOS: Mathematics #Homotopy and Cohomology in Algebraic Topology

paper · pdf · doi:10.48550/arxiv.1708.06009

openalex publication_date 2017/08/20 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

With G = ℤ/p, p prime, we calculate the ordinary G-cohomology (with Burnside ring coefficients) of ℂP_G^∞ = 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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