Timeline for Invariant cohomology vs cohomology of quotient
Current License: CC BY-SA 4.0
6 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| May 10, 2023 at 23:50 | comment | added | David Loeffler | Yes, this is the Cartan-Leray spectral sequence. If memory serves, there is a nice account of it in the book "A User's Guide to Spectral Sequences" by McCleary. | |
| May 10, 2023 at 19:49 | comment | added | abx | @Mark Grant: Yes, you are right: after browsing through the internet, the name usually used seems to be "Cartan-Leray". | |
| May 10, 2023 at 18:51 | comment | added | Mark Grant | Just a comment on terminology: I think the name "Hochschild-Serre spectral sequence" is usually reserved for the spectral sequence associated to a group extension. Since $M$ need not be aspherical here, we just have a covering, and I've seen this called the "Cartan-Leray spectral sequence". | |
| May 10, 2023 at 16:16 | comment | added | abx | Well... The result does not hold if you replace $\mathbb{Z}$ by $\mathbb{Z}^2$, say, so there is something to prove. Now there might be a more down-to-earth argument. But let me say that the Hochschild-Serre spectral sequence is a fairly standard (and quite efficient) tool in this kind of questions. | |
| May 10, 2023 at 15:39 | comment | added | Mattis Bakken | Thanks! I have to be honest that I don't understand that argument since I'm not yet familiar with this theory. Honest question: is that argument a bit overkill and there is a more direct down-to-earth way to see it, or is that really the way to go? | |
| May 10, 2023 at 15:30 | history | answered | abx | CC BY-SA 4.0 |