Timeline for First Chern class of a specific line bundle
Current License: CC BY-SA 3.0
10 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| S Mar 2, 2018 at 23:06 | history | bounty ended | truebaran | ||
| S Mar 2, 2018 at 23:06 | history | notice removed | truebaran | ||
| Mar 2, 2018 at 23:06 | vote | accept | truebaran | ||
| Feb 27, 2018 at 12:20 | answer | added | Johannes Nordström | timeline score: 6 | |
| S Feb 23, 2018 at 0:38 | history | bounty started | truebaran | ||
| S Feb 23, 2018 at 0:38 | history | notice added | truebaran | Canonical answer required | |
| Feb 17, 2018 at 17:46 | comment | added | Arun Debray | Ah, of course; sorry about that. One way to do that would be to prove it for the universal bundle over $\mathit{BSpin}^c$, but there ought to be an easier proof. | |
| Feb 17, 2018 at 13:58 | comment | added | truebaran | This is exactly my point: I would like to prove that $w_2(E)$ is precisely mod 2 reduction of $c_1(L_E)$.In order to prove this I managed to show that both sides are natural wih respect to pullbacks and both side vanish on spin bundles. The remaning part is that this mod 2 reduction does not vanish if the bundle is not spin and this boils down to my original question. So how you can show that $w_2(E)$ is mod 2 reduction of $c_1(L_E)$? | |
| Feb 17, 2018 at 3:54 | comment | added | Arun Debray | Since $E$ is a spin^c bundle, $w_2(E)$ is the mod 2 reduction of $c_1(L_E)$ (here $w_2$ is the second Stiefel-Whitney class). $w_2$ is precisely the obstruction for a spin structure, so since $E$ is not spin, $w_2(E)\ne 0$, and hence $c_1(L_E)$ is odd. | |
| Feb 16, 2018 at 23:30 | history | asked | truebaran | CC BY-SA 3.0 |