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Please use this identifier to cite or link to this item: http://hdl.handle.net/1807/19047

Title: Pre-quantization of the Moduli Space of Flat G-bundles
Authors: Krepski, Derek
Advisor: Meinrenken, Eckhard
Selick, Paul
Department: Mathematics
Keywords: Symplectic Geometry
Homotopy Theory
Issue Date: 18-Feb-2010
Abstract: 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.
URI: http://hdl.handle.net/1807/19047
Appears in Collections:Doctoral
Department of Mathematics - Doctoral theses

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