If $G$ is a discrete group, recall that a (naive) $G$-spectrum consists of based $G$-spaces $E_n$ together with based $G$-maps $\Sigma E_n \to E_{n+1}$, where we give the suspensio …

I am teaching a graduate seminar in equivariant topology. The format of the course is that I will give 2-3 weeks of background lectures, then each week a student will present a to …

I'm doing some work with model categories and operads, and to check a certain hypothesis I've had to learn a bit of equivariant homotopy theory. Let $M$ be a model category and $G$ …

Suppose we are given a diagram of topological spaces. We can restrict ourselves to the diagrams over finite partially ordered sets and let all spaces be good enough (e.g. CW-comple …

Let $G$ be a (nice enough) topological group (actually a filtered colimit of compact Lie groups), and let $X$ be a manifold with an action (a proper one in fact) by a Lie group $H$ …

I know very little about the fancy equivariant stable homotopy category, so I apologize if this question is silly for one reason or another, but: I think that stable homotopy, in …

Let $E$ be a spectrum. Then $E \wedge E$ is a $\mathbb{Z}/2$-spectrum in the naivest possible sense, i.e., an object with $\mathbb{Z}/2$-action in the (∞,1)-category of spec …

For a finite group $G$, let $O_G$ denote the orbit category of $G$. Is there a explicit/nice description of cofibrations in the functor category $Top^{O_G^{op}}$ where the weak equ …

Suppose a finite group $G$ acts piecewise linearly on a polyhedron $X$. Then there are two kinds of equivariant cohomology (or homology). $\bullet$ With coefficients in a $\Bbb Z …

I'm looking for simple examples of calculations of equivariant homology and of equivariant bordism. I have a finite group G acting on an CW-complex X. I would like to calculate t …

As shown by Lewis, May, and McClure (MR0598689), the ordinary equivariant Bredon cohomology theory $H^*_G(-; M)$ extends to an $RO(G)$-graded cohomology theory precisely when the c …

I'm trying to learn a bit about equivariant homotopy theory. Let G be a compact Lie group. I guess there is a cofibrantly generated model category whose objects are (compactly ge …

Let $G$ be a finite group. I wonder whether the following statement is true, known and written down: There is a t-structure on the stable $G$-equivariant homotopy category such th …

Let $G$ be a compact connected simply connected Lie group. Let $LG$ be the corresponding loop group. What is the cohomology of its classifying space (i.e. what is the equivariant c …

Is there a condition for a $G$-equivariant map $X \to Y$ to be a cofibration of $G$-spaces? Here $X$ and $Y$ are CW complexes, the group $G$ is finite, and acts by cellular maps. …