# Questions tagged [equivariant-homotopy]

Equivariant homotopy theory is the study of how homotopy theory behaves when spaces are considered together with a group action on them.

141 questions
Filter by
Sorted by
Tagged with
230 views

1 vote
73 views

### Equivariant spectrum with coefficients

I am curious to know whether spectra with coefficients as defined in Adams's Blue book be defined to an equivariant setting. In the non-equivariant case, for a spectrum $E$ and an abelian group $A$, ...
169 views

### Rational G-spectrum and geometric fixed points

For a finite group $G$, how is a rational $G$-spectrum $X$ detected by the geometric fixed point functor $\phi^H$ where we consider the conjugacy class of $H\leq G$? I tried finding a reference for ...
75 views

252 views

### What is the pointed Borel construction of the $0$-sphere?

From what I understand, the Borel construction takes a $G$-space $X$ and produces a topological space $X\times_{G}\mathbf{E}G$―the homotopy quotient $X/\!\!/G$ of $X$ by $G$ in the $\infty$-category ...
43 views

### Projective resolution of a dual coefficient system

I was trying to read the paper "Equivariant minimal models" by G. Triantafillou(1982) and was trying to compute cohomology of a system of DGA with rational coefficient system. Given a finite ...
423 views

202 views

### Computing homotopy colimit of a space with free $S^1$-action

Context. I am trying to understand the argument in B.4 of Thomas Nikolaus, Peter Scholze, On topological cyclic homology, arXiv:1707.01799 (on p147). I am still lost. But from Maxime's helpful ...
$\DeclareMathOperator{\Fix}{\operatorname{Fix}}$I am looking for any reference regarding the following problem: Problem: Consider a smooth almost-free action of $S^1$ on a smooth sphere $S^n$. Then ...