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arXiv · 0708.1269

Pre-quantization of the Moduli Space of Flat G-Bundles over a Surface

Derek Krepski
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Abstract

For a simply connected, compact, simple Lie group G, the moduli space of flat G-bundles over a closed surface is known to be pre-quantizable at integer levels. For non-simply connected G, however, integrality of the level is not sufficient for pre-quantization, and this paper determines the obstruction -- namely a certain cohomology class in H^3(G^2;Z) -- that places further restrictions on the underlying level. The levels that admit a pre-quantization of the moduli space are determined explicitly for all non-simply connected, compact, simple Lie groups G.

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Derek Krepski. 2008-09-29. Pre-quantization of the Moduli Space of Flat G-Bundles over a Surface. https://doi.org/10.1016/j.geomphys.2008.07.009

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