2010/04/13 by Derek Krepski, Krepski, Derek
Mathematics · #Advanced Algebra and Geometry #Algebraic Topology (math.AT) #FOS: Mathematics #Geometry and complex manifolds #Homotopy and Cohomology in Algebraic Topology #Symplectic Geometry (math.SG) #math.AT #math.SG
paper · pdf · doi:10.48550/arxiv.1004.2286
135 pages, 4 figures
arxiv created 2010/04/13 · openalex publication_date 2010/04/13 · arxiv updated 2010/04/15 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
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 sufficient conditions for the pre-quantization of MG(Σ), the moduli space of flat G-bundles over a closed surface Σ. For a simply connected, compact, simple Lie group G, MG(Σ) 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 cohomology class in H3(G× G;\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. Partial results are obtained for the case of a surface Σ 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 pre-quantization coincide.