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

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

2007-08-09

arxiv.org/abs/0708.1269v2

Mathematics

Symplectic Geometry

28 pages, 1 table, new version contains minor corrections, to be published in Journal of Geometry and Physics

Scientific paper

10.1016/j.geomphys.2008.07.009

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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