This thesis studies the pre-quantization of quasi-Hamiltonian group actions from a
cohomological viewpoint. The compatibility of pre-quantization with symplectic reduction
and the fusion product are established, and are used to understand the necessary and sufficient conditions for the pre-quantization of M(G,S), the moduli space of
at flat G-bundles over a closed surface S.
For a simply connected, compact, simple Lie group G, M(G,S) 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 thesis determines the obstruction, namely a certain 3-dimensional cohomology class, 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. Partial results are obtained for the case of a surface S with marked points.
Also, it is shown that via the bijective correspondence between quasi-Hamiltonian
group actions and Hamiltonian loop group actions, the corresponding notions of prequantization coincide.
| Identifer | oai:union.ndltd.org:LACETR/oai:collectionscanada.gc.ca:OTU.1807/19047 |
| Date | 18 February 2010 |
| Creators | Krepski, Derek |
| Contributors | Meinrenken, Eckhard, Selick, Paul |
| Source Sets | Library and Archives Canada ETDs Repository / Centre d'archives des thèses électroniques de Bibliothèque et Archives Canada |
| Language | en_ca |
| Detected Language | English |
| Type | Thesis |
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