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Equivariant homotopy theory is the study of how homotopy theory behaves when spaces are considered together with a group action on them.
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homotopy invariant and coinvariant
Let $V$ be a chain complex, which is either $Z$ or $Z/2$ graded. A circle action on $V$ is
by definition an action of the dga $H_\ast(S^1)$. This consists of a map $D : V → V$ , which is of square zer …