Nuclear dimension of simple stably projectionless C*-algebras

Abstract

We prove that Z-stable, simple, separable, nuclear, non-unital C*-algebras have nuclear dimension at most 1. This completes the equivalence between finite nuclear dimension and Z-stability for simple, separable, nuclear, non-elementary C*-algebras.

40 pages. Fixed a typo in the statement of Theorem 2.7. Analysis & PDE, to appear