Timeline for Compute characteristic classes of principal bundle over closed surfaces
Current License: CC BY-SA 3.0
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| Nov 7, 2017 at 12:41 | comment | added | Tobias Diez | Well, it is kind of like in Chern-Weil theory. There you integrate the curvature over the 2-dimensional fundamental polygon. However, now that everything is discrete, this integral has to be replaced with the holonomy of the boundary curve. Now the "holonomy" is $\hat{\beta}$ and the boundary curve $J$. Admittedly, this reasoning is a bit heuristic but should give you a general idea (sorry, I don't have the time right now for a more detailed answer). | |
| Nov 6, 2017 at 15:05 | comment | added | YYF | Actually, I asked this question exactly because I was reading Atiyah and Bott's paper. Therefore, could you explain why $\hat{\beta}(J)$ is the characteristic class of the bundle? They didn't offer many details actually. | |
| Nov 6, 2017 at 12:12 | history | answered | Tobias Diez | CC BY-SA 3.0 |