Classification of $\mathcal {O}_\infty $-Stable $C^*$-Algebras

James Gabe, University of Southern Denmark, Odense, Denmark.

• Chapters1. Introduction and main results2. Equivalence of $\ast $-homomorphisms3. Approximate domination and nuclearity4. $\mathcal O_2$-stable and $\mathcal O_\infty $-stable $\ast $-homomorphisms5. Absorbing representations6. Asymptotic intertwining7. A unitary path and some key lemmas8. The Kirchberg-Phillips Theorem9. Strongly $\mathcal O_\infty $-stable $\ast $-homomorphisms10. Ideals and actions of topological spaces11. Absorbing representations revisited12. Ideal-related $KK$-theory13. A stable uniqueness theorem14. An ideal-related $\mathcal O_2$-embedding theorem15. The main theorems