The $C_2$-equivariant ordinary cohomology of $BT^2$

Steven R. Costenoble; Thomas Hudson

The $C_2$-equivariant ordinary cohomology of $BT^2$

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arxiv 2411.06470 v1 pith:QHP5BUYB submitted 2024-11-10 math.AT

Steven R. Costenoble , Thomas Hudson This is my paper · ORCID

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keywords cohomologyordinaryallowsburnsidecalculatecalculatedcapturecase

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abstract

We calculate the ordinary $C_2$-cohomology of $BT^2$ with Burnside ring coefficients, using an extended grading that allows us to capture a more natural set of generators. We discuss how this cohomology is related to those of $BT^1$ and $BU(2)$, calculated previously, both relationships being more complicated than in the nonequivariant case.

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Parametrized $\underline{\mathbb{F}}_2$-Cohomology of $B_{C_2}O(1)$
math.AT 2026-07 conditional novelty 7.0 of 10

The RO(ΠP)-graded F2-cohomology of P=B_{C2}O(1) is the explicit ring M2[u10,u11,a10,a11,e,ν] with u10u11=ue, a10u11+a11u10=ae, e2=ν2=1.

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