Timeline for On the smoothness of transition functions
Current License: CC BY-SA 4.0
5 events
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| Jun 9, 2020 at 17:22 | comment | added | alexpglez98 | Mmm, I see that I have to study more to completely understand it. The analyticity property of the action means that the action can be recovered by the Taylor coefficients? Is it necessary the action to be transtitive? You've mentioned that $(G,F)$ is a homogeneus space. Do you have any recommendation to read these properties about Jets and group actions? | |
| Jun 9, 2020 at 16:51 | comment | added | Ben McKay | That is the idea. But you only need to compute Taylor series up to some finite order to get this to work. The group action cannot fix a point and fix an analytic coordinate system at that point without fixing all nearby points. The Hilbert basis theorem can prove that the subgroup fixing that point can only fix a finite number of Taylor coefficients of a coordinate system without fixing all points in the connected component of that point. At least when there are finitely many components to the homogeneous space, this should do the trick. I think there is a way to deal with infinite components. | |
| Jun 9, 2020 at 16:37 | vote | accept | alexpglez98 | ||
| Jun 9, 2020 at 16:47 | |||||
| Jun 9, 2020 at 16:35 | comment | added | alexpglez98 | Thanks. I'm not familiar with Jets enough to undesrtand it, but I think I catch the idea. Is it like calculate the "Taylor expansion" on $s$ of $g(x)\cdot s$ and recover $g(x)$? | |
| Jun 9, 2020 at 11:31 | history | answered | Ben McKay | CC BY-SA 4.0 |