2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/152244We prove several versions of "quantization commutes with reduction" for circle actions on manifolds that are not symplectic. Instead, these manifolds possess a weaker structure, such as a spin^c structure. Our theorems work whenever the quantization data and the reduction data are compatible; this condition always holds if we start from a presymplectic (in particular, symplectic) manifold.LaTeX 2e, 28 pagesDifferential Geometrytext