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arXiv · 1404.4840

A K-homological approach to the quantization commutes with reduction problem

Yanli Song
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Abstract

Kasparov defined a distinguished K-homology fundamental class, so called the Dirac element. We prove a localization formula for the Dirac element in K-homology of crossed product of C^{*}-algebras. Then we define the quantization of Hamiltonian G-spaces as a push-forward of the Dirac element. With this, we develop a K-homological approach to the quantization commutes with reduction theorem.

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Yanli Song. 2014-10-09. A K-homological approach to the quantization commutes with reduction problem. https://arxiv.org/abs/1404.4840

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