A new proof of the Kirchberg–Phillips theorem that unifies the stably finite and purely infinite classification frameworks and recovers Kirchberg's Geneva theorems as corollaries.
KK-rigidity of simple nuclear C*-algebras
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abstract
It is shown that if $A$ and $B$ are unital separable simple nuclear $\mathcal Z$-stable C$^*$-algebras and there is a unital embedding $A \rightarrow B$ which is invertible on $KK$-theory and traces, then $A \cong B$. In particular, two unital separable simple nuclear $\mathcal Z$-stable C$^*$-algebras which either have real rank zero or unique trace are isomorphic if and only if they are homotopy equivalent. It is further shown that two finite strongly self-absorbing C$^*$-algebras are isomorphic if and only if they are $KK$-equivalent in a unit-preserving way.
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A unified approach for classifying simple nuclear $C^\ast$-algebras
A new proof of the Kirchberg–Phillips theorem that unifies the stably finite and purely infinite classification frameworks and recovers Kirchberg's Geneva theorems as corollaries.