On the asymptotic homotopy type of inductive limit \(C^*\)-algebras. (English) Zbl 0791.46047

Let \(X\), \(Y\) be compact, connected, metrisable spaces with base points \(x_ 0\), \(y_ 0\) and let \({\mathcal K}\) denote the compact operators. It is shown that \(C_ 0(X\setminus x_ 0)\otimes {\mathcal K}\) is asymptotically homotopic (or shape equivalent) to \(C_ 0(Y\setminus y_ 0)\otimes {\mathcal K}\) if and only if \(X\) and \(Y\) have isomorphic \(K\)-groups. Similar results are obtained for certain inductive limits of nuclear \(C^*\)- algebras.


46L80 \(K\)-theory and operator algebras (including cyclic theory)
46L85 Noncommutative topology
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