Timeline for Lift Lie group action on a small neighborhood
Current License: CC BY-SA 3.0
6 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Oct 4, 2016 at 8:26 | vote | accept | DLIN | ||
| Jul 25, 2016 at 13:48 | comment | added | Ben McKay | Maybe it is easier to picture that the dimension of the $G$-orbit at a point $m \in M$ is the dimension of the set of vectors $v(m)$ for $v \in \mathfrak{g}$. This is in standard textbooks, like Abraham and Marsden. Pick as many vector fields $v_i \in \mathfrak{g}$ as you can which are linearly independent at $m$, and they remain so nearby. | |
| Jul 25, 2016 at 13:38 | answer | added | Friedrich Knop | timeline score: 6 | |
| Jul 25, 2016 at 13:27 | comment | added | DLIN | I do not follow, the rank is no continuous. Why the rank of vanishing Lie algebra is zero nearby? Sorry@BenMcKay | |
| Jul 25, 2016 at 13:23 | comment | added | Ben McKay | Local freedom is clear: look at the rank of elements of the Lie algebra vanishing at each point. Since the rank is zero along $N$, it is zero nearby. | |
| Jul 25, 2016 at 12:48 | history | asked | DLIN | CC BY-SA 3.0 |