On the asymptotic homotopy type of inductive limit \(C^*\)-algebras
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.
inductive limits of nuclear \(C^*\)-algebras
scientific article; zbMATH DE number 537337