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Almost complex structures and geometric quantization

David Borthwick·Alejandro Uribe
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Abstract

We study two quantization schemes for compact symplectic manifolds with almost complex structures. The first of these is the Spin-c quantization. We prove the analog of Kodaira vanishing for the Spin-c 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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BibTeXRIS

David Borthwick, Alejandro Uribe. 1996-08-17. Almost complex structures and geometric quantization. https://arxiv.org/abs/dg-ga/9608006

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