Timeline for Non-trivial topological line bundles over cartesian product of manifolds not coming from a pullback
Current License: CC BY-SA 3.0
7 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Mar 28, 2013 at 11:35 | history | edited | Liviu Nicolaescu | CC BY-SA 3.0 |
edited body
|
| Mar 28, 2013 at 9:29 | history | edited | Liviu Nicolaescu | CC BY-SA 3.0 |
edited body
|
| Mar 27, 2013 at 23:32 | comment | added | Eric Wofsey | Complex line bundles are classified by $H^2$ (with coefficients in $\mathbb{Z}$), so you can get extra line bundles on a product that come from $H^1(X)\otimes H^1(Y)$. The simplest example of this is for $X=Y=S^1$: every complex line bundle on $X$ or $Y$ is trivial, but $H^2(X\times Y)=\mathbb{Z}$. | |
| Mar 27, 2013 at 22:20 | comment | added | Hugo Chapdelaine | Ok, I was being idiot | |
| Mar 27, 2013 at 21:38 | vote | accept | Hugo Chapdelaine | ||
| Mar 27, 2013 at 21:38 | comment | added | Hugo Chapdelaine | I see, so this explains why I was not able to construct such an example. What about complex line bundle? | |
| Mar 27, 2013 at 20:25 | history | answered | Liviu Nicolaescu | CC BY-SA 3.0 |