Timeline for How to build the principal SU(2) bundles on surfaces?
Current License: CC BY-SA 2.5
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| Feb 22, 2010 at 15:10 | comment | added | Paul | I don't see what is wrong with the statement that the trivial bundle is the only bundle up to bundle isomorphism. But (as everywhere in mathematics) the existence of non-trivial automorphisms implies that there is ambiguity in choosing an identification of your object with a fixed object. Actually, in this case (SU(2) bundle over a 2-manifold), the group of bundle automorphisms is path connected, and so any two identifications of your bundle with the trivial bundle are homotopic, so you get a little bit more "canonicalness" than in general. | |
| Feb 22, 2010 at 4:55 | comment | added | Theo Johnson-Freyd | Although there is only one bundle up to isomorphism, it's wrong to say that it "is" the trivial bundle: there's no canonical isomorphism between a given SU(2) bundle and the trivial bundle, but rather the space of such isomorphisms is a torsor over the group of sections of the trivial bundle. | |
| Feb 22, 2010 at 2:03 | history | answered | Paul | CC BY-SA 2.5 |