m, n)$?

Current License: CC BY-SA 4.0

15 events

when toggle format	what		by	license	comment
Mar 5, 2021 at 14:41	answer	added	John Rognes		timeline score: 2
Feb 19, 2021 at 23:05	answer	added	John Rognes		timeline score: 9
S Dec 17, 2020 at 23:04	history	bounty ended	CommunityBot
S Dec 17, 2020 at 23:04	history	notice removed	CommunityBot
S Dec 9, 2020 at 21:29	history	bounty started	Michael Albanese
S Dec 9, 2020 at 21:29	history	notice added	Michael Albanese		Draw attention
Aug 26, 2020 at 1:39	comment	added	John Greenwood		@DylanWilson well played, sir
Aug 26, 2020 at 1:27	comment	added	Dylan Wilson		@JohnGreenwood nice! but I guess there's a negative answer for n=k=0 !
Aug 25, 2020 at 21:36	history	edited	Michael Albanese	CC BY-SA 4.0	Edited to maintain consistency.
Aug 25, 2020 at 7:28	comment	added	John Greenwood		Along with $m=2$, there is also a positive answer for $n=1$ :)
Aug 24, 2020 at 21:23	comment	added	Dylan Wilson		sorry- I deleted my previous answer because I can't seem to make it work without basically just doing the whole computation anyway... maybe one needs to extract something from the Cartan seminar? It would be nice if there was a clean argument like Tim's though... Messing around it seems like $\mathbb{Z}/m[B\mathbb{Z}]\to\mathbb{Z}/m[B\mathbb{Z}/m]$ has an $\mathbb{E}_{\infty}$-$\mathbb{Z}/m$-retract? (which would do it) But I don't really trust that I didn't obscure some error while doing that... if I end up trusting that, I will update the post.
Aug 24, 2020 at 18:44	comment	added	Tim Campion		Maybe for context one should point out that for stable cohomology operations, the answer is yes. That is, any map of spectra $\Sigma^n H\mathbb Z \to \Sigma^{n+k} H\mathbb Z / m$ commutes with multiplication by $m$ (which is null on $\Sigma^{n+k} H\mathbb Z / m$), and so descends, via the cofiber sequence $\Sigma^n H\mathbb Z \xrightarrow m \Sigma^n H\mathbb Z \to \Sigma^n H\mathbb Z / m$, to a map $\Sigma^n H\mathbb Z / m \to \Sigma^{n+k} H\mathbb Z / m$.
Aug 24, 2020 at 17:45	history	edited	Michael Albanese	CC BY-SA 4.0	Edited title so that it is consistent with the question (which was edited earlier)
Aug 24, 2020 at 13:23	history	edited	Phil Tosteson	CC BY-SA 4.0	Changed notation to avoid confusion with m-adics
Aug 24, 2020 at 13:10	history	asked	Michael Albanese	CC BY-SA 4.0