Timeline for Interesting contexts in which the first few cohomology groups ($H^1$ and $H^2$) show up?
Current License: CC BY-SA 4.0
8 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Jan 11 at 23:07 | audit | Low quality posts | |||
| Jan 11 at 23:09 | |||||
| Jan 6 at 10:00 | audit | Reopen votes | |||
| Jan 6 at 10:12 | |||||
| Dec 14, 2023 at 13:59 | answer | added | Lukas Heger | timeline score: 3 | |
| Dec 14, 2023 at 13:25 | answer | added | Derek Holt | timeline score: 1 | |
| Dec 14, 2023 at 12:50 | comment | added | Hilbert Jr. | @DerekHolt also, are you by any chance you D.F. Holt, author of a 1979 paper on the interpretation of $H^n$ via crossed sequences? | |
| Dec 14, 2023 at 12:48 | comment | added | Hilbert Jr. | @DerekHolt could you elaborate in what way? I see how an automorphism produces a derivation, but I don't yet fully see what the equivalence relation on automorphisms should be. Should it just be "$\varphi\sim\psi$ if and only if there exists $a\in A$ such that $\varphi(x)\psi(x)^{-1}=i(a^{px}a^{-1})$ for all $x\in E$" (where $p:E\to G$ is part of the extension)? I don't really see the usefulness of this equivalence relation. | |
| Dec 14, 2023 at 12:22 | comment | added | Derek Holt | $H^1(G,A)$ also arises in studying automorphisms of extensions of $A$ by $G$. | |
| Dec 14, 2023 at 11:00 | history | asked | Hilbert Jr. | CC BY-SA 4.0 |