Quantization of presymplectic manifolds and circle actions

da Silva, Ana; Karshon, Yael; Tolman, Susan

doi:10.1090/S0002-9947-99-02260-6

Quantization of presymplectic manifolds and circle actions
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by Ana Cannas da Silva, Yael Karshon and Susan Tolman PDF

Trans. Amer. Math. Soc. 352 (2000), 525-552 Request permission

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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