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I tried to compute Bredon cohomology of $\mathbb{S}^\sigma$, where $\sigma$ is a sign representation of $\mathbb{Z}/2$, following first chapter and first construction of cohomology from Bredon's "Equi …

My question refers to Tyler Lawson's answer to this question: Computing Bredon Cohomology of Z/2-spheres? Namely, I have a problem with understanding 0'th degree. From my calculation it seems that $H …

In Mike Hill's paper "On the Algebras over Equivariant Little Disks" ( https://arxiv.org/abs/1709.02005) in section 2.2 there is an information, that algebras over $\mathcal{D}(\sigma)$, that is littl …

I have a problem with understanding Cohen's definition, as written in "The Homology of Iterated Loop Spaces" by Cohen, Lada and May (Part III, chapter 5, at the end of chapter). So in order to define …

Is it possible to replace cellular chains in the construction of Bredon homology/cohomology with cingular chains? (Possible it should be, but in that case will the Bredon homology groups be the same?) …

I'll answer this question just for future references. Since (after fixing a coefficient system) the ordinary cohomology theory is unique, on G-CW-complexes cohomology defined by cellular chains will b …

I am working on understanding Peter May's "A genaral algebraich approach to Steenrod operations", so for this purpose I am trying to compare his framework with explicit construction of Steenrod square …

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 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 …

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 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'm procedding with understanding Greenlees's paper "The Four Approaches to Cohomology Theories with Reality": https://arxiv.org/abs/1705.09365 Problem concerns the section 1.D. Consider the cofiber …

Let $E^r$ be a commutative Hopf algebra homology spectral sequence over $\mathbb{Z}/p$, i.e. such that every sheet is a commutative Hopf algebra. I am struggling with proving (probably simple) fact …

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 …