Timeline for Classification of $O(2)$-bundles in terms of characteristic classes
Current License: CC BY-SA 3.0
6 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Mar 26, 2016 at 17:42 | comment | added | Denis Nardin | @Bilateral I've written an answer expanding the point, since a proper response didn't fit in this margin :) | |
| Mar 26, 2016 at 16:53 | comment | added | Bilateral | @DenisNardin: Thanks for the pointer. Could you please elaborate a little bit on your answer? The references dealing with the Postnikov tower seem to be quite specialized. | |
| Mar 26, 2016 at 13:37 | vote | accept | Bilateral | ||
| Mar 26, 2016 at 13:37 | comment | added | Bilateral | @MarkGrant: Thanks. I think your description fits with what I get by considering the Cech cocycle defined by $O(2)$, which, when decomposed in terms of $O(2) = SO(2)\rtimes\mathbb{Z}_{2}$ gives rise to the Stiefel-Whitney class $w_{1}$ of $O(2)$ and some 2-cohomology class which locally takes values in $\mathbb{Z}_{2}$. | |
| Mar 26, 2016 at 13:02 | comment | added | Denis Nardin | In general if you want to study $G$-bundles you should take a look at the Postnikov tower of $BG$. Unfortunately this tower is often infinite (so you'll need an infinite number of twisted characteristic classes) | |
| Mar 26, 2016 at 10:01 | history | answered | Mark Grant | CC BY-SA 3.0 |