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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 …

$\DeclareMathOperator{\Hom}{Hom}$ 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 am trying to understand basic notions from Hill-Hopkins-Ravenel paper: https://arxiv.org/abs/0908.3724 In the Example 3.10 we are considering equviariant cellular chain complex for $n$-dimensional …

$\DeclareMathOperator{\Tot}{Tot}$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 …

In one of the very first sentences in Hovey's "Model Categories", Ist chapter, we read that One can always invert these "weak equivalences" formally , but there is a foundational prob …

I am reading now Tyler Lawson's $E_n$ ring spectra and Dyer-Lashof operations form the Handbook of Homotopy Theory and I've got a question on the Remark 1.4.19. We have an operad $\mathcal{O}$ and $\ …

I moved this question from Math StackExchange. I am trying to compute homology of $Conf(n, \mathbb{R}^2)$ - ordered configurations of $n$ points on the plane - using Serre spectral sequence. I know t …

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 …

I am going through Milnor and Moore - On the structure of Hopf algebras (MSN) (I have already posted one question on that, another one is coming). My question is about Proposition 4.9, more specifica …

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 …

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 am trying to understand some part of J. Greenlees's "Four approaches to cohomology theories with reality": https://arxiv.org/abs/1705.09365 I have a problem with understanding $RO(Q)$-graded homoto …

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 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 …

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 …