Timeline for Tangent bundle of a homogeneous space and the euler exact sequence
Current License: CC BY-SA 3.0
5 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Mar 18, 2016 at 8:35 | vote | accept | Saal Hardali | ||
| Mar 15, 2016 at 12:27 | answer | added | Andreas Cap | timeline score: 11 | |
| Mar 11, 2016 at 13:44 | comment | added | Peter Michor | See 18.16 (p 225) of mat.univie.ac.at/~michor/dgbook.pdf | |
| Mar 11, 2016 at 13:42 | comment | added | Jason Starr | If you are working in the setting of algebraic geometry, you can prove that isomorphism via "faithfully flat descent". If you pullback your exact sequence to $G$, then it is the tangent bundle sequence. Next you check that the induced isomorphism between the pullback to $G$ of $T(G/H)$ and $G\times^H (\mathfrak{g}/\mathfrak{h})$ satisfies a "cocycle condition" after pullback to $G \times_{G/H} G \cong H \times G$. Thus the isomorphism of bundles on $G$ is the pullback of an isomorphism on $G/H$. | |
| Mar 11, 2016 at 13:23 | history | asked | Saal Hardali | CC BY-SA 3.0 |