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Results tagged with equivariant-homotopy
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user 43054
Equivariant homotopy theory is the study of how homotopy theory behaves when spaces are considered together with a group action on them.
12
votes
Accepted
Definition of $Fun^G( \mathcal C, \mathcal D)$ in the setting of quasicategories
A(n ∞-)category with $G$-action is just a functor $BG\to \mathrm{Cat}_∞$. Then, if $\mathcal{C},\mathcal{D}$ are (∞-)categories with $G$-action, we can get another (∞-)category with $G$ action $\mathr …
- 16.5k
9
votes
Accepted
"Oriented representation" sphere
First of all, note that right before example 3.9 they prove that
$$H^G_*(S^V;\underline{\mathbb{Z}})=H_*(C^{cell}_*(S^V)^G)\,,$$
where $C^{cell}_*(S^V)$ is the cellular complex for some $G$-CW-structu …
- 16.5k
9
votes
Accepted
Applications of equivariant homotopy theory in chromatic homotopy theory
The canonical answer to this question is of course the celebrated solution by Hill, Hopkins and Ravenel to the Kervaire invariant one problem
Hill, Michael A., Michael J. Hopkins, and Douglas C. Rave …
- 16.5k
4
votes
Accepted
Is a $G$-cell complex always a $G$-CW complex?
As Najib says in the comments to the question, the proof of the classical statement can be easily-ish adapted to the equivariant case. Let's see the details
Lemma Let $X$ be a $G$-CW-complex and let …
- 16.5k