Localization C∗-algebras and 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 K K i ( A ,...

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Bibliographic Details
Published inJournal of homotopy and related structures Vol. 18; no. 1; pp. 1 - 22
Main Authors Wang, Hang, Zhang, Chaohua, Zhou, Dapeng
Format Journal Article
LanguageEnglish
Published Berlin/Heidelberg Springer Berlin Heidelberg 01.03.2023
Springer Nature B.V
Subjects
Algebra
Algebraic Topology
Functional Analysis
Localization
Mathematics
Mathematics and Statistics
Number Theory
Index pairing
homology
46L80
58B34
Localization algebra
19K35
19K56
theory
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Summary: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 K K i ( A , B ) and the localization algebra description of K K i ( A , B ) and show that the two pairings are compatible.
ISSN:2193-8407
1512-2891
DOI:10.1007/s40062-022-00320-z