Prequantization of quasi symplectic groupoids - Quintero, Stiven Ramírez (2025)
This dissertation addresses the prequantization of quasi symplectic groupoids, expanding the framework of classical symplectic geometry. The main objective is to establish the conditions for the prequantization of these groupoids, characterized by a multiplicative 2-form on the space of arrows and twisted by a closed 3-form on the base space. The study demonstrates that prequantization is feasible if the combined form is an integral 3-cocycle and the 3-form on the base space is exact. Furthermore, the dissertation explores Morita invariance in prequantization and its implications for Hamiltonian spaces associated with quasi symplectic groupoids. Examples, such as the prequantization of the cotangent bundle, illustrate the practical application of the theory.