Almost Complex Structures and Geometric Quantization
نویسندگان
چکیده
We study two quantization schemes for compact symplectic manifolds with almost complex structures. The first of these is the Spinc quantization. We prove the analog of Kodaira vanishing for the Spinc Dirac operator, which shows that the index space of this operator provides an honest (not virtual) vector space semiclassically. We also introduce a new quantization scheme, based on a rescaled Laplacian, for which we are able to prove strong semiclassical properties. The two quantizations are shown to be close semiclassically.
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