Contractible Cuntz classes in $Z$-stable C${}^{\ast }$-algebras

Abstract

Let $A$ be a unital, simple and Z-stable C${}^{\ast }$-algebra. We show that the set of positive elements in $A$ (resp. $A\otimes K$) belonging to a fixed non-compact Cuntz class is contractible as a topological subspace of $A$ (resp. $A\otimes K$). In light of earlier work by Zhang, Jiang and Hua in the compact case, we deduce a complete calculation of the homotopy groups of Cuntz classes for these algebras.

13 pages, no figures