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Quantization of Presymplectic Manifolds and Circle Actions

Ana Canas da Silva·Yael Karshon·Susan Tolman
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Abstract

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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Ana Canas da Silva, Yael Karshon, Susan Tolman. 1997-05-17. Quantization of Presymplectic Manifolds and Circle Actions. https://arxiv.org/abs/dg-ga/9705008

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