Timeline for Why do homotopy theorists care whether or not $BP$ is $E_\infty$?
Current License: CC BY-SA 3.0
8 events
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| Aug 25, 2016 at 9:39 | comment | added | Sean Tilson | I see my confusion!! The construction of Basterra-Mandell is some idempotent as opposed to the Quillen idempotent. Thanks for pointing this out. | |
| Aug 24, 2016 at 17:48 | comment | added | Peter May |
Sean, I said Basterra and Mandell. The paper is The multiplication on $BP$" and the abstract reads in full: $BP$ is an $E_4$ ring spectrum. The $E_4$ structure is unique up to automorphism
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| Aug 24, 2016 at 11:35 | comment | added | Sean Tilson | It is worth pointing out that if $BP$ is $E_{\infty}$ then Andy Baker has constructed it (if I recall correctly). arxiv.org/abs/1204.4878 Also, @PeterMay, is this arxiv.org/pdf/1310.3336v1.pdf the reference you had in mind with your above comment about the Quillen idempotent being $E_4$? I don't recall them getting more than $E_3$, but maybe you mean a different paper. | |
| Aug 16, 2016 at 21:38 | comment | added | Peter May | I doubt there is a consensus. It is $E_4$ compatibly with $MU$, but if it is $E_{\infty}$, then it only is so incompatibly with $MU$. I have no strong feeling, but I would hazard a guess that it is not $E_{\infty}$. | |
| Aug 16, 2016 at 20:35 | comment | added | CWcx | @PeterMay, what is the general belief amongst homotopy theorists regarding an answer to this question? Is there evidence pointing one way or the other? | |
| Aug 15, 2016 at 23:16 | comment | added | Peter May | Well certainly one wants the category of $BP$-modules to be symmetric monoidal under the smash product, which won't come from $E_1$, and one wants to know how which Dyer-Lashof operations are preserved from $MU$ (not all, of course). | |
| Aug 15, 2016 at 12:00 | comment | added | Denis Nardin | Just a personal curiosity, but do you know of any application that requires $BP$ to be more than $E_1$? | |
| Aug 14, 2016 at 22:27 | history | answered | Peter May | CC BY-SA 3.0 |