Timeline for square root of diffeomorphism of R: does it always exist?
Current License: CC BY-SA 2.5
8 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Apr 10, 2011 at 19:59 | comment | added | André Henriques | I looked it up (Proposition 3.3.1 of Pressley and Segal's book): The rotation by $1/n$ is in the image of the exponentional map $exp:Vect(S^1)\to Diff(S^1)$ and its preimage under that map is huge. It contains all $1/n$-periodic vector fields whose integral over $S^1$ is $n$. [Note: here I'm using the model $S^1:=\mathbb R/\mathbb Z$] | |
| Mar 31, 2011 at 14:09 | answer | added | rpotrie | timeline score: 2 | |
| Mar 28, 2011 at 18:52 | comment | added | André Henriques | It's not even locally injective?!? How do you see that? | |
| Mar 26, 2011 at 23:57 | comment | added | Allen Knutson | This is reminding me of the statement that the exponential map from $Vec(S^1)$ to $Diff(S^1)$ is neither locally injective nor surjective (from "Loop Groups"). | |
| Mar 23, 2011 at 16:49 | vote | accept | André Henriques | ||
| Mar 23, 2011 at 15:44 | answer | added | Sergei Ivanov | timeline score: 19 | |
| Mar 23, 2011 at 14:51 | answer | added | user9072 | timeline score: 9 | |
| Mar 23, 2011 at 13:52 | history | asked | André Henriques | CC BY-SA 2.5 |