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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.
10
votes
Why are equivariant homotopy groups not RO(G)-graded?
I would like to add a few points:
You can define $RO(G)$-graded homotopy groups of $G$-spectra, see for example Stefan Schwede's course notes on equivariant homotopy theory.
These groups are intere …
8
votes
$RO(G)$-graded homotopy groups vs. Mackey functors
I can answer your first question in some special cases.
Let $p$ be a prime and $G=C_p$ the cyclic group of order $p$. If $p=2$, the answer to your question is yes and if $p$ is odd, then it is no.
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