Timeline for Given a complex vector bundle with rank higher than 1, is there always a line bundle embedded in it?
Current License: CC BY-SA 4.0
9 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Dec 8, 2020 at 8:37 | answer | added | Denis Nardin | timeline score: 8 | |
| Dec 7, 2020 at 20:07 | history | became hot network question | |||
| Dec 7, 2020 at 16:17 | history | edited | Daniele Tampieri | CC BY-SA 4.0 |
Embedded link and minor grammar corrections
|
| Dec 7, 2020 at 13:16 | review | Close votes | |||
| Dec 14, 2020 at 3:09 | |||||
| Dec 7, 2020 at 12:28 | answer | added | David E Speyer | timeline score: 36 | |
| Dec 7, 2020 at 12:27 | comment | added | Igor Belegradek | A (complex) line bundle over $X$ is determined by its first Chern class in $H^2(X)$. In particular, if $H^2(X)=0$, then every line bundle over $X$ is trivial. On the other hand, such $X$ can admit a nontrivial complex vector bundle, e.g. if $\pi_i(U(n))$ is nontrivial, there is a nontrivial $\mathbb C^n$-bunlde over $S^{i+1}$. | |
| Dec 7, 2020 at 12:10 | comment | added | David E Speyer | As a help for other people working on this question: The context is $C^{\infty}$ vector bundles on smooth manifolds. | |
| Dec 7, 2020 at 12:07 | review | First posts | |||
| Dec 7, 2020 at 12:15 | |||||
| Dec 7, 2020 at 12:05 | history | asked | Sunhf | CC BY-SA 4.0 |