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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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Equivariant Homotopy
Let $G=\mathbb{Z}/2\mathbb{Z}$ be $\{\pm1\}$ and let there be two $G$-spaces given: $X=$ The surface of a cylinder including its boundary circles and $S^4$. That means we two G-actions $f_1:G\times X\ …