Localization C*-algebras and index pairing

作者：Wang, Hang^*; Zhang, Chaohua; Zhou, Dapeng

来源：JOURNAL OF HOMOTOPY AND RELATED STRUCTURES, 2023, 18(1): 1-22.

DOI：10.1007/s40062-022-00320-z

• K-homology
• K K -theory
• Localization algebra
• K-theory
• Index pairing

Kasparov KK-theory for a pair of C*-algebras (A,B) can be formulated equivalently in terms of the K-theory of Yu's localization algebra by Dadarlat-Willett-Wu. We investigate the pairings between K-theory K-j(A) and the two notions of KK-theory which are Kasparov KK-theory KKi(A,B) and the localization algebra description of KKi(A,B) and show that the two pairings are compatible.