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

作者：Song Yanli^*

来源：Journal of Geometry and Physics, 2017, 112: 29-44.

DOI：10.1016/j.geomphys.2016.08.017

• Geometric quantization
• K-homology
• Cross product
• Localization

Kasparov (1988) 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. Published by Elsevier B.V.

• 出版日期2017-2