Timeline for State of knowledge on the Commutative W-spaces which appear in "Model Categories of Diagram Spectra"
Current License: CC BY-SA 3.0
6 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Feb 14, 2019 at 18:52 | vote | accept | David White | ||
| Aug 21, 2012 at 15:49 | comment | added | Peter May | Gut feelings of my collaborators and myself. But also the technical point that we doubted that the map $$(E\Sigma_j)_+ \wedge_{\Sigma_j} X^{(j)}\longrightarrow X^{(j)}/\Sigma_j$$ is an equivalence for cofibrant $W$-spaces $X$. | |
| Aug 15, 2012 at 0:48 | comment | added | David White | Thanks for your speedy reply. I agree that this information makes the question less interesting. You mentioned in your answer to my previous question that you didn't think commutative $W$-rings would have a model structure (this opinion also comes up in MMSS, but without attribution). Since the Lawson paper is relatively new, could you sketch why you originally didn't think commutative $W$-rings would have a model structure? I was hoping to draw you out on this with my comment in the question above about "soft evidence." I would have asked on the other thread, but it seemed off topic. | |
| Aug 11, 2012 at 16:46 | comment | added | Peter May | I hadn't thought about that, since to me the answer to the second question makes the first question uninteresting. With the obvious definitions, if you had a model structure then there would be a Quillen adjunction to commutative symmetric or orthogonal spectra that is not a Quillen equivalence. It seems more likely to me that you just don't get a model structure. But it is murky. Unclear what kind of prolongation you get from commutative orthogonal spectra when you know they can't give you what they ought to give you. | |
| Aug 11, 2012 at 16:02 | comment | added | David White | Thanks for the answer, I will definitely check that paper out. This completely answers the second question. Does it also mean you can't have a model structure on commutative $W$-rings induced from the one on $W$-spaces? I.E. if there was such a model structure, would it have to give a homotopy category equivalent to that of commutative symmetric ring spectra? | |
| Aug 11, 2012 at 13:58 | history | answered | Peter May | CC BY-SA 3.0 |