Timeline for Pontryagin dual of a group-cohomology class
Current License: CC BY-SA 4.0
7 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Jul 12, 2023 at 8:39 | comment | added | Andrea Antinucci | Thanks. Perfect! | |
| Jul 12, 2023 at 8:39 | vote | accept | Andrea Antinucci | ||
| Jul 11, 2023 at 7:50 | history | edited | Achim Krause | CC BY-SA 4.0 |
added 1466 characters in body
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| Jul 11, 2023 at 7:45 | comment | added | Achim Krause | I've augmented the post with a direct argument why $-\varepsilon^\vee$ is the correct cocycle (note the sign, which I messed up yesterday) | |
| Jul 10, 2023 at 17:05 | comment | added | Andrea Antinucci | Thank you! By "using injectivity of $\mathbb{R}/\mathbb{Z}$" do you mean the fact that any symmetric cocycle valued in $\mathbb{R}/\mathbb{Z}$ is a coboundary? Also, is it obvious that $\epsilon ^\vee$ constructed in this way is the cocycle associated with the Pontryagin dual of the original short exact sequence? | |
| Jul 10, 2023 at 16:00 | comment | added | Achim Krause | Some intuition: By construction, $\overline{\varepsilon}$ is additive in the $A^\vee$ argument. If we could choose $\beta$ also additive in the $A^\vee$ argument, it would show that $\varepsilon$ is a coboundary. The $\overline{\varepsilon^\vee}$ term measures how $\beta$ fails to be additive in the $A^\vee$ argument, hence has something to do with $\varepsilon$ being nontrivial. | |
| Jul 10, 2023 at 15:40 | history | answered | Achim Krause | CC BY-SA 4.0 |