Timeline for Is every additive cohomology operation stable?
Current License: CC BY-SA 4.0
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| Aug 30, 2023 at 4:08 | history | bumped | CommunityBot | This question has answers that may be good or bad; the system has marked it active so that they can be reviewed. | |
| May 2, 2023 at 3:07 | history | bumped | CommunityBot | This question has answers that may be good or bad; the system has marked it active so that they can be reviewed. | |
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| Apr 12, 2021 at 0:12 | answer | added | Tim Campion | timeline score: 1 | |
| Mar 24, 2021 at 19:27 | comment | added | Bad English | I'm stupid and have to correct my comment on Q1. Contrary, the answer seems to be "yes" also. I suppose that primitive elements of free commutative Hopf-algebra over F_p are given exactly by p-th powers of (primitive) generators. It is easy to see dualizing everything and consider this thing as divided powers-algebra over F_p. Hence they are actually obtained by applying stable operations to fundamental class. | |
| Mar 24, 2021 at 19:11 | comment | added | Bad English | 1'. That's true. Again this follows from the description of the cohomology ring. This also holds over integers coefficients. | |
| Mar 24, 2021 at 19:10 | comment | added | Bad English | 1. No. Cohomology of EM-spaces are free polynomial algebras over all stable operations (which are admissible merely by degree reasons) applied to the fundamental class, generators are primitive with respect to the loop-space structure (a.k.a addition), thus the p-th power followed by any stable-operation is additive | |
| Mar 24, 2021 at 18:10 | comment | added | Harry Wilson | Personally, I'd rename Q4 as Q3' | |
| Mar 24, 2021 at 17:36 | comment | added | Tim Campion | @ConnorMalin Presumably you're right -- that answers Question 3! | |
| Mar 24, 2021 at 17:18 | comment | added | Connor Malin | Aren't the Adams operations an example of additive cohomology operations that are not stable? | |
| Mar 24, 2021 at 16:10 | history | edited | Tim Campion | CC BY-SA 4.0 |
added 265 characters in body
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| Mar 24, 2021 at 16:04 | comment | added | Maxime Ramzi | Sorry I deleted my comment because I got confused for a second.But yeah, the thing you denote $St$ isn't "really" stable cohomology operations, there's a lot of things in the kernel | |
| Mar 24, 2021 at 16:02 | comment | added | Tim Campion | @MaximeRamzi Er... of course you're right, there's something wrong with the way I've set things up. I think your proposal is probably the right fix -- there is a natural map $St \to Unst^{add}$ and the question is whether it's a surjection. | |
| Mar 24, 2021 at 15:36 | history | asked | Tim Campion | CC BY-SA 4.0 |