Unsuspended Connective $E$-Theory

Abstract

We prove connective versions of results by Shulman [Shu10] and Dadarlat-Loring [DL94]. As a corollary, we see that two separable $C^*$-algebras of the form $C_0(X) \otimes A$, where $X$ is a based, connected, finite CW-complex and $A$ is a unital properly infinite algebra, are $\bu$-equivalent if and only if they are asymptotic matrix homotopy equivalent.