Localization C*-algebras and K-theoretic duality
Marius Dadarlat, Rufus Willett, Jianchao Wu
TL;DR
This paper offers a new perspective on KK-theory by representing it through time-parametrized families of operators that asymptotically commute with certain representations, building on Yu's localization algebras.
Contribution
It introduces a novel approach to KK-theory using localization algebras and asymptotic commutation, expanding the theoretical framework.
Findings
Provides a new interpretation of KK-theory
Connects localization algebras with asymptotic operator families
Enhances understanding of operator asymptotics in KK-theory
Abstract
Based on the localization algebras of Yu, and their subsequent analysis by Qiao and Roe, we give a new picture of KK-theory in terms of time-parametrized families of (locally) compact operators that asymptotically commute with appropriate representations.
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