Timeline for Are $H^3(A,U(1))$ and $\operatorname{Ext}^1(A,A^\vee)$ isomorphic for $A$ finite Abelian?
Current License: CC BY-SA 4.0
4 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Jul 23 at 14:49 | vote | accept | Andrea Antinucci | ||
| Jul 23 at 14:49 | |||||
| Jul 23 at 8:08 | comment | added | Dave Benson | There is no surjective natural transformation. I've explained why in a separate answer. | |
| Jul 22 at 14:19 | comment | added | Andrea Antinucci | Ok thanks. Is there at least a map $H^3(A,\mathbb{R}/\mathbb{Z})\rightarrow \text{Ext}^1(A,A^\vee)$? From your answer it cannot be injective of course. The purpose of this question is to understand if all 3d DW action are $2\pi i \int a\cup \beta(a)$, but indeed I realized that putting a coefficient in front, say $2\pi i n \int a\cup \beta(a)$, cannot always be reabsorbed into $\beta$ giving a $\beta '$ for a different extension. So maybe would be enough to have a surjective map. | |
| Jul 22 at 13:37 | history | answered | André Henriques | CC BY-SA 4.0 |