Timeline for Is a closed basic 2-form on a principal $S^1$ bundle the curvature of a connection?
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| Oct 12, 2016 at 6:46 | comment | added | Ben McKay | If all of these integrals have integer values, then indeed $F$ is the curvature of some connection, but perhaps not on the circle bundle you started with. If $F$ has the same integrals as the Chern form of your circle bundle, then of course $F$ differs from the Chern form by an exact differential $d\phi$ and you add (a suitable constant multiple of) $\phi$ to your connection form to get curvature $F$. | |
| Oct 12, 2016 at 6:36 | history | answered | Ben McKay | CC BY-SA 3.0 |