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While writing a grant proposal I faced a problem of justification my area of interest to a broader audience. So I thought it would be nice to ask it here: What are applications/impact of computations …

$\require{AMScd}$ Dear all, I have a question concerning Charles Rezk's paper "A model for the homotopy theory of homotopy theory ", precisely Proposition 7.6 in this paper. It is proven there that if …

I am going through V. Hinich's "Lectures on Infinity Categories" and I have a (possibly trivial) question on Segal spaces. We define Segal space to be a bisimplicial set $X$ which is fibrant in Reedy …

$\DeclareMathOperator{\Hom}{Hom}$ Dear all, The question is for teaching purposes and rather basic, so I hope that it also allows (relatively) easy answer. By abstract homotopy theory we know that if …

I have the following problem. It is well known that $H^\ast(D_8,\mathbb{Z}/2)\cong \mathbb{F}_2[x,y,w]/(xy=0)$ with $|x|=|y|=1$ and $|w|=2$ (see Adem,Milgram "Cohomology of finite groups"). So we get …

$\DeclareMathOperator{\Tot}{Tot}$I have the following problem. Let $H$ and $G$ be groups such that $H$ acts on $G$, i.e., there exists a group homomorphism $H\to \mathrm{Aut}(G)$ and let $M$ be an abe …

I have the following problem. Let $\mathcal{C}_0$, $\mathcal{C}$ be small categories and $\mathcal{D}$, $\mathcal{E}$ be locally small categories. Let $Q\colon \mathcal{C}_0\to \mathcal{C}$ be a funct …

I asked this question on the homotopy theory chat, but I haven't got any answer - thus I decided to post it as a question here. The question is rather historical. Let $X$ be a connected topological sp …

This is a follow-up to this question: Reduction to graph subgroups for Bredon homology when the $G_1\times G_2$ is $G_2$-free In his (very nice) answer Gregory Arone stated the following fact. Let $Q: …

I have the following problem. Let $\Gamma_{G_1\times G_2}$ be a full subcategory of the orbit category $\mathcal{O}_{G_1\times G_2}$ consisting of graph subgroups of $G_1\times G_2$. Further, let $N$ …

Some time ago I cam across the paper "What we still don't know about loop spaces of spheres" by Ravenel: https://people.math.rochester.edu/faculty/doug/mypapers/loop.pdf which concerns computing Morav …

I am reading through the calculations in Hu-Kriz "Real-oriented homotopy theory and an analogue of the Adams-Novikov spectral sequence" and I've got a small problem in understanding the computations o …

I would like to have proper references in a paper that I'm writing down. This concerns computations of the coefficients of equivariant Eilenberg-MacLane spectra over the cyclic group of order 2 (denot …

I have the following problem. Let $Q$ denote $\mathbb{Z}/2$ as an abelian group and let $X$ be a $Q$-spectrum. If I want to compute the homotopy groups of $X^{hQ}$, homotopy fixed points spectrum, I c …

I am looking for a digitalized version of paper by J.P. May and J. McClure A reduction of Segal conjecture, as I need it to understand some lemma from Kuhn's Tate Cohomology and Periodic Localization …