A -homological approach to the quantization commutes with reduction problem

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• 作者：Yanli Song ^{ylsong@me.com}
• 关键词：Geometric quantization ; K-homology ; Cross product ; Localization
• 刊名：Journal of Geometry and Physics
• 出版年：2017
• 出版时间：February 2017
• 年：2017
• 卷：112
• 期：Complete
• 页码：29-44
• 全文大小：528 K
• 卷排序：112

文摘

Kasparov (1988) defined a distinguished KK-homology fundamental class, so called the Dirac element. We prove a localization formula for the Dirac element in KK-homology of crossed product of C∗C∗-algebras. Then we define the quantization of Hamiltonian GG-spaces as a push-forward of the Dirac element. With this, we develop a KK-homological approach to the quantization commutes with reduction theorem.