A K-Theoretic Note on Geometric Quantization
Abstract
Description
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.
11 pages, LaTeX 2e using amsmath, xypic
11 pages, LaTeX 2e using amsmath, xypic