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A K-Theoretic Note on Geometric Quantization

David S. Metzler
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Abstract

We show that the results of the paper Symplectic Reduction and Riemann-Roch for Circle Actions of Duistermaat, Guillemin, Meinrenken and Wu can be expressed entirely in K-theory. We show that their quantization is simply a pushforward in K-theory, and use Lerman's symplectic cutting and the localization theorem in equivariant K-theory to prove that quantization commutes with reduction. Only the case where the action is free on the zero level set of the moment map is addressed.

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David S. Metzler. 1998-09-07. A K-Theoretic Note on Geometric Quantization. https://arxiv.org/abs/math/9809031

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