\(KK\)-equivalence for amalgamated free product \(C^*\)-algebras. (English) Zbl 1404.46047
Summary: We prove that any reduced amalgamated free product \(C^\ast\)-algebra is \(KK\)-equivalent to the corresponding full amalgamated free product \(C^\ast\)-algebra. The main ingredient of its proof is Julg-Valette’s geometric construction of Fredholm modules with Connes’s view for representation theory of operator algebras.