Quantization of Presymplectic Manifolds and Circle Actions

Details Quantization of Presymplectic Manifolds and Circle Actions Quantization of Presymplectic Manifolds and Circle Actions

1997-05-17

arxiv.org/abs/dg-ga/9705008v1

Mathematics

Differential Geometry

LaTeX 2e, 28 pages

Scientific paper

We 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.

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