arXiv math/98090311998-09-07math.SGmath.KT

A K-Theoretic Note on Geometric Quantization

David S. Metzler

备注：: 11 pages, LaTeX 2e using amsmath, xypic

英文摘要：

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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