Homotopy Theory

12:00 AM

StackOverflow seems to be trying to address its diversity and general "attitude" problem:

Stack Overflow Isn’t Very Welcoming. It’s Time for That to Change.

Jay Hanlon on April 26, 2018

Let’s start with the painful truth:

Too many people experience Stack Overflow¹ as a hostile or elitist place, especially newer coders, women, people of color, and others in marginalized groups.

Our employees and community have cared about this for a long time, but we’ve struggled to talk about it publicly or to sufficiently prioritize it in recent years. And results matter more than intentions.

Now, that’s not because most Stack Overflow contributors are hostile jerks. The majority of them are generous and kind. Sure, a few are… just generous, I guess? But our active users regularly express thei …

There's a link to a survey at the bottom of that article, in case you want to be involved in the conversation.

skull

12:28 AM

522

Q: Does Stack Exchange really want to conflate newbies with women/people of color?

The Stack Overflow Isn’t Very Welcoming blog post says: Too many people experience Stack Overflow as a hostile or elitist place, especially newer coders, women, people of color, and others in marginalized groups. There have been accusations of elitism against SO since time immemorial. Basic...

Eric Peterson

12:41 AM

for all intents and purposes, you should treat me as almost completely ignorant of what 'structured ring spectrum' even means

Jonathan Beardsley

@skull yeah this really brings out of some of the worst people on the SE network.

Eric Peterson

here's a slightly refined question, which i think y'all have started answering in pieces: where can i read about the kinds of operations one finds on the homology of a structured ring spectrum, ideally leading up to an assertion of the rough form "there is a monad T on graded v.s.es over F_2 s.t. H_(E) is a T-algebra when E is an E_n-alg, and if E = F(X) is the free E_n-algebra on an S-mod X, then H_ E = T H_* X"?

Jonathan Beardsley

I don't really have any interest in engaging with that meta post.

Or even really engaging with people about any aspect of it in here. I maybe posted it so people could read it and possibly take the survey, and I know people in here have had non-trivial concerns about that.

If you want to have a serious discussion about it I'm willing to talk elsewhere.

Eric Peterson

it's also 100% possible i'm not even asking the right question: part of what i really want to do is to take a 2-torsion homotopy class in a particular such E_n-algebra spectrum which lifts a 2-torsion integral homology class, cone it off without leaving the world of E_n-algebras, and understand something about the integral homology of the resulting spectrum

i'm already suffering the 2-adic bockstein spectral sequence, so i figure asking about the behavior of the steenrod algebra on the mod-2 homology is both more concrete & still in the window of what i'm after

but 'add an E_n-cell designed to kill a 2-torsion class' might be further from 'free E_n-alg on Susp^k M(2)' than i think

Dylan Wilson

2:51 AM

@EricPeterson without any structure at all, 'coning of a 2-torsion class' sounds to me like coning off a map from a sphere, still. Coning off a map from M(2) would, on homology, kill the hurewicz image of the class and its bockstein. Is that what you want to do?

also, the H-infinity book has a description of the homology of a free E_infty algebra on a spectrum on page 298 (you can also find this in lots of places)

for E_n-algebras, in the case of spaces, you can find a purported answer in cohen-lada-may in cohen's chapter, but it should be taken with some grains of salt- there are lots of mistakes in the specifics in that chapter if you want to use it for computations

Tyler Lawson

3:24 AM

the operations that appear for E_n-algebras also appear, phrased in ring spectrum terms, starting on page 64 of the H_infty book

it's also right to be a little bit nervous about adding the E_n-cell. if the spectrum you're adding the cell to is R, then the free E_n-way to kill off this map M(2) -> R has homology that's pretty confusing

there's a filtration on it whose associated graded is the coproduct, in the category of algebras over the monad T that you want, of H_* R with T(H_* M(2))

n=1 is a good case for poking at this

let's say H_* M(2) is generated by x and y (where P_1 y = x)

then T is the "associative algebra" monad, and H_*(R) is an associative algebra. then the associated graded takes H_*(R) and freely adjoins new, noncommuting, algebra generators x and y

but the d_1 differential in this associated graded takes x and hits the class you attached it to

Tyler Lawson

3:46 AM

when n > 1 you don't have the noncommutativity problem, but you do have the Browder bracket, and your happiness wrt that may depend on how much you enjoy shifted restricted Lie algebras

Peter Nelson

5:20 AM

@EricPeterson The first paragraph of Charles' Congruence Criterion paper (arxiv.org/pdf/0902.2499.pdf) rephrases results of the H_\infty book to give more or less exactly this statement for the E_\infty case (and tells you where to find it in the H_\infty book)

(oh, Charles points to the same place that Dylan did)

Peter Nelson

5:34 AM

Sections 5-11 or so of his notes (faculty.math.illinois.edu/~rezk/power-operation-lectures.dvi) for the course that resulted in that paper might also be helpful

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