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.
$C_2$-equivariant Homology Operations: Results and Formulas
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abstract
In this note we state corrected and expanded versions of our previous results on power operations for $C_2$-equivariant Bredon homology with coefficients in the constant Mackey functor on $\mathbb{F}_2$. In particular, we give a version of the Adem relations. The proofs rely on certain results in equivariant higher algebra which we will supply in a longer version of this paper.
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Parametrized $\underline{\mathbb{F}}_2$-Cohomology of $B_{C_2}O(1)$
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.