Localization C*-algebras and K-theoretic duality

Jianchao Wu  (Penn State University)

13:00 pm to 14:00 pm, December 26th, 2016   Science Building A1510

Abstract:

One of the most remarkable features of Gennadi Kasparov's KK-theory is the various equivalent ways to define it. Depending on the context and usage, cycles in this theory can be realized as Fredholm modules (in the spirit of index theory), generalized homomorphisms ¨¤ la Cuntz, (completely positive and suspended) asymptotic morphisms, etc. Based on the localization algebras of Guoliang Yu, and their subsequent analysis by Yu Qiao and John Roe, we give a new picture of KK-theory in terms of time-parametrized families of (locally) compact operators that asymptotically commute with the given $C^\ast$-algebras. This is joint work with Marius Dadarlat and Rufus Willett.