Timeline for Lagrangian torus fibrations and Arnol'd-Liouville theorem
Current License: CC BY-SA 4.0
5 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Jul 9, 2019 at 5:15 | vote | accept | John Rached | ||
| Jul 9, 2019 at 4:39 | answer | added | Jonny Evans | timeline score: 7 | |
| Jul 9, 2019 at 4:18 | comment | added | John Rached | Ah, thank you very much! That makes perfect sense. | |
| Jul 9, 2019 at 4:12 | comment | added | abx | The Arnold-Liouville theorem gives you a canonical isomorphism of the trivial bundle $T_q(Q)\times F_q$ over $F_q$ with the cotangent bundle $T^*(F_q)$. Since $F_q$ is a torus, this cotangent bundle is naturally isomorphic to the trivial bundle $\Omega \times F_q$, where $\Omega $ is the space of invariant differential 1-forms on $F_q$. But the de Rham theorem gives a canonical isomorphism $\Omega \overset{\sim}{\longrightarrow}H^1(F_q,\mathbb{R})$. | |
| Jul 9, 2019 at 2:16 | history | asked | John Rached | CC BY-SA 4.0 |