Timeline for Does the maximal compact subgroup always act transitively on a compact homogeneous space?
Current License: CC BY-SA 4.0
10 events
| when toggle format | what | by | license | comment | |
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| Feb 14, 2022 at 17:18 | answer | added | Ian Gershon Teixeira | timeline score: 0 | |
| Nov 19, 2021 at 19:57 | vote | accept | Ian Gershon Teixeira | ||
| Nov 19, 2021 at 16:48 | answer | added | Francois Ziegler | timeline score: 4 | |
| Nov 19, 2021 at 16:36 | comment | added | Ian Gershon Teixeira | Anyway since any Zariski closed subgroup has finitely many connected components Corollary 2 subsumes the answer from YCor. In particular Corollary 2 states that as long as $ H $ has finitely many connected components then $ G/H $ is acted on transitively by a maximal compact subgroup. | |
| Nov 19, 2021 at 16:32 | comment | added | Ian Gershon Teixeira | Oh wow this article is absolute little 3 page gem exactly what I wanted you could honestly just post it as an answer and it would be great. Here's a link that worked better for me ams.org/journals/proc/1950-001-04/S0002-9939-1950-0037311-6/… | |
| Nov 19, 2021 at 16:13 | comment | added | Francois Ziegler | The result about simply connected homogeneous spaces quoted in your (currently) last paragraph is Montgomery’s Theorem (1950). | |
| Nov 19, 2021 at 16:05 | history | edited | Ian Gershon Teixeira | CC BY-SA 4.0 |
added 1544 characters in body
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| Nov 19, 2021 at 5:44 | comment | added | YCor | So yes, I thinks $KH$ holds when $G$ is real algebraic and $H$ is Zariski-closed cocompact. For $G=KAN$ and $H$ then contains a conjugate of $AN$. | |
| Nov 19, 2021 at 5:40 | comment | added | YCor | You're asking when $K$ acts transitively on $G/H$, and (for every group $G$ and subgroups $K,H$) this holds iff $KH=G$. | |
| Nov 19, 2021 at 4:51 | history | asked | Ian Gershon Teixeira | CC BY-SA 4.0 |