What is the equivariant (co)homology of the rotation action of $S^1=SO(2)$ on $\mathbb{R}^2$?
2026-03-25 23:58:42.1774483122
Equivariant (co)homology of the rotation action of the circle on the plane
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$\Bbb R^2$ is equivariantly contractible, so it has the same cohomology as $H^*_{SO(2)}(pt) = H^*(CP^\infty)$.