Oh okay, and in that paper it's clear that they're using the wedge product, not the Cartesian product.

Phew...

@GijsHeuts Ah thanks Gijs

@Jon Sorry, I should have specified. I meant the wedge product

@GijsHeuts Actually the paper you linked to seems to be answering the converse question: i.e. when Σ Tot(Y) is equivalent to Y as an associative comonoid. This seem to imply the statement I was after (Tot(ΣX)=X) for X 1-connected, but I'm wondering if it holds more generally

is there something i can use to visualize A(2)_*//A(0)_*?

i could draw it by hand but it's 32-dimensional so i'd rather not

@skd: what are you hoping for?

@skd luckily other people have drawn A(2) for you! There are some links to pictures after the references here: ms.uky.edu/~guillou/suminar11.html

tho maybe you're asking about something else.

thanks! I'm looking to understand A-subcomodules of A(2)_//A(0)_ (and hopefully spectrally realize some of them) @JohnPalmieri

I once ran across an interactive online drawing of A(2) but I don't remember who created this

i forget exactly what the // means but i think there's also a picture of A(2) after killing Sq^1 there, by bert

the interactive thing is by bob bruner, i think

oh, and niles johnson: nilesjohnson.net/Aof2

thanks! this is very helpful

I don't really understand the picture of A(2)/Sq^1, or maybe I don't know what it means. If it's the quotient by the 2-sided ideal generated by Sq^1, then maybe it's okay, but not if it's the quotient by the left ideal generated by Sq^1 (which is what skd is looking for).

yeah, i don't think that drawing answers my question sadly. as you said i'm interested in A(2)/A(2)*Sq^1 (so it's not given by that diagram since it isn't 32-dimensional)

but with some tedious work i can deduce the drawing from the bruner-johnson interactive diagram