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Homotopy theory, homological algebra, algebraic treatments of manifolds.

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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 …
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