{"paper":{"title":"Ph. D. Thesis: Pre-quantization of the moduli space of flat G-bundles","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.AT"],"primary_cat":"math.SG","authors_text":"Derek Krepski","submitted_at":"2010-04-13T23:10:13Z","abstract_excerpt":"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 $M_G(\\Sigma)$, the moduli space of flat $G$-bundles over a closed surface $\\Sigma$. For a simply connected, compact, simple Lie group $G$, $M_G(\\Sigma)$ 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"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1004.2286","kind":"arxiv","version":1},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/1004.2286/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"}