The $C_2$-equivariant ordinary cohomology of $BU(2)$

Steven R. Costenoble; Thomas Hudson

The $C_2$-equivariant ordinary cohomology of $BU(2)$

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arxiv 2411.06411 v1 pith:EMSDT2H3 submitted 2024-11-10 math.AT math.AG

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

classification math.ATmath.AG

keywords allowsequivariantbundlescharacteristiccohomologycomplexdefineordinary

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abstract

We calculate the ordinary $C_2$-cohomology, with Burnside ring coefficients, of $BU(2)$, the classifying space for $C_2$-equivariant complex 2-plane bundles, using an extended grading that allows us to capture a more natural set of generators. This allows us to define characteristic classes for such bundles. Combined with earlier calculations, it also allows us to define characteristic numbers for equivariant complex lines and surfaces and we give some sample computations.

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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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