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Journal of Operator Theory

Volume 71, Issue 1, Winter 2014  pp. 285-294.

Unsuspended connective $E$-theory

Authors Otgonbayar Uuye
Author institution: School of Mathematics, Cardiff University, Cardiff, CF24 4AG, UK

Summary:  We develop an unsuspended version of connective $E$-theory and prove connective versions of results by D\u{a}d\u{a}rlat--Loring and Shulman. 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 connective $E$-theory equivalent if and only if they are asymptotic matrix homotopy equivalent.

Keywords:  noncommutative shape theory, $K$-theory, $KK$-theory, $E$-theory

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