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

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

Chapters 1. Introduction and main results 2. Equivalence of $\ast $-homomorphisms 3. Approximate domination and nuclearity 4. $\mathcal O_2$-stable and $\mathcal O_\infty $-stable $\ast $-homomorphisms 5. Absorbing representations 6. Asymptotic intertwining 7. A unitary path and some key lemmas 8. The Kirchberg-Phillips Theorem 9. Strongly $\mathcal O_\infty $-stable $\ast $-homomorphisms 10. Ideals and actions of topological spaces 11. Absorbing representations revisited 12. Ideal-related $KK$-theory 13. A stable uniqueness theorem 14. An ideal-related $\mathcal O_2$-embedding theorem 15. The main theorems