Timeline for Palais's and Kobayashi's theorems on automorphism groups of geometric structures
Current License: CC BY-SA 4.0
12 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Apr 18, 2023 at 11:47 | answer | added | Ben McKay | timeline score: 1 | |
| S Mar 23, 2022 at 10:03 | history | bounty ended | CommunityBot | ||
| S Mar 23, 2022 at 10:03 | history | notice removed | CommunityBot | ||
| Mar 22, 2022 at 22:02 | answer | added | Chris Wendl | timeline score: 2 | |
| Mar 16, 2022 at 19:24 | answer | added | Peter Michor | timeline score: 1 | |
| S Mar 15, 2022 at 8:10 | history | bounty started | Chris Wendl | ||
| S Mar 15, 2022 at 8:10 | history | notice added | Chris Wendl | Improve details | |
| Mar 11, 2022 at 17:20 | comment | added | Chris Wendl | I would say the most natural topology on Diff(M) in this situation is $C^\infty_{loc}$, i.e. uniform convergence of all derivatives on compact subsets. For G this will of course be equivalent to the topology that it inherits from its identification with an orbit in M. | |
| Mar 11, 2022 at 13:37 | comment | added | Tobias Diez | What topology do you want to consider on $Diff(M)$ if $M$ is not closed? | |
| Mar 11, 2022 at 13:36 | comment | added | Tobias Diez | I don't have time right now for a detailed answer, so only a few observations for now. In arxiv.org/abs/1501.06269, section II.2 (especially Corollary II.2.3) the Lie group structure of a normal subgroup is extended to a Lie group structure on the ambient group. This seems to correspond to your basic lemma. Moreover, the proof of Theorem IV.4.16 seems to follow very closely the strategy you have outlined above (but of course here $G=Diff$ is not a Banach Lie group). | |
| Mar 9, 2022 at 14:26 | answer | added | Nicolast | timeline score: 2 | |
| Mar 9, 2022 at 13:39 | history | asked | Chris Wendl | CC BY-SA 4.0 |