Timeline for Does $\mathrm{SO}(3)$ act faithfully on a countable set?
Current License: CC BY-SA 4.0
6 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Sep 10, 2021 at 13:32 | comment | added | Uri Bader | Related: mathoverflow.net/q/269008/89334 | |
| Sep 7, 2021 at 22:09 | vote | accept | Erik Walsberg | ||
| Sep 6, 2021 at 8:49 | answer | added | YCor | timeline score: 17 | |
| Sep 6, 2021 at 2:50 | answer | added | Will Sawin | timeline score: 30 | |
| Sep 6, 2021 at 0:15 | comment | added | Will Sawin | $SO(3)$ embeds into $SO_3(\mathbb C)$. Using choice, fix an isomorphism between $\mathbb C$ and $\overline{\mathbb Q_p}$, giving an isomorphism between $SO_3(\mathbb C)$ and $SO_3(\overline{\mathbb Q_p})$. Then doesn't $SO_3(\overline{\mathbb Q_p})$ act faithfully on $SO_3(\overline{\mathbb Q_p})/SO_3(\overline{\mathbb Z_p})$, which is countable because it is the union over all finite extensions $K_p$ of $\mathbb Q_p$ with ring of integers $\mathcal O_{K_p}$ of the countable $SO_3(K_p)/ SO_3(\mathcal O_{K_p})$? | |
| Sep 6, 2021 at 0:01 | history | asked | Erik Walsberg | CC BY-SA 4.0 |