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|Title: ||Pre-quantization of the Moduli Space of Flat G-bundles|
|Authors: ||Krepski, Derek|
|Advisor: ||Meinrenken, Eckhard|
|Keywords: ||Symplectic Geometry|
|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.|
|Appears in Collections:||Doctoral|
Department of Mathematics - Doctoral theses
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