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Tom Bachmann
Tom Bachmann
9:11 AM
@JeremyHahn I'd also like to know the answer to this. This is claimed to be possible on page 1 here: cambridge.org/core/journals/…
... but I'm a little bit suspicious about such a statement without proof. I have worked out some of the details that go into this and can send you my notes, but it is far from pretty.
 
 
4 hours later…
Saal Hardali
Saal Hardali
12:46 PM
@JeremyHahn Wait, so how do we know that Johnson Wilson theory E(n) is homotopy commutative? Maybe we don't?
 
 
3 hours later…
Charles Rezk
Charles Rezk
3:54 PM
@SaalHardali Well $E(n)$ is Landweber exact, so we can exactly compute things like $E(n)^*(E(n)\wedge E(n))$, and presumably thus show directly that $E(n)$ is homotopy commutative.
 
Saal Hardali
Saal Hardali
4:12 PM
@CharlesRezk Oh, yeah silly me that works. Its just I always thought of E(n) as something you get directly out of BP, so i was thrown off a bit.
 
Drew
Drew
I guess the argument is along the lines of it has a homotopy commutative multiplication up to phantom maps, but all phantoms vanish by a result of Hovey-Strickland. This is possibly already all in the K(n)-local book
 
Charles Rezk
Charles Rezk
4:45 PM
Knowing that phantom maps vanish follows once you have that $E(n)^\ast(E(n)\wedge E(n)) \approx \mathrm{Hom}_{E(n)_\ast}(E(n)_\ast E(n), E(n)_\ast)$, which presumably comes out of the direct computation.
 
 
3 hours later…
Andrea Marino
Andrea Marino
7:25 PM
Hi guys! I'd like to thank you for the precious mathematical support you gave me for my master thesis!! Here it is what you contributed to: https://www.researchgate.net/publication/334469225_-Operadic_methods_towards_Factorization_Homology

Feel free to share it, maybe as a soft introduction to this kind of stuff (there's also acknowledgments to you, btw :) )
 

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