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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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Why is the oriented $G$-homotopy type of a $G$-complex uniquely determined by the periodicit...
Say we have a periodicity generator $e \in H^k(BG)$. I can show that we then have a $(k-1)$-dimensional $G$-complex $X$ with free $G$-action. It's also not that difficult to see that it has trivial $G …