Spanier–Whitehead K-duality for C∗-algebras

Abstract

Classical Spanier–Whitehead duality was introduced for the stable homotopy category of finite CW complexes. Here we provide a comprehensive treatment of a noncommutative version, termed Spanier–Whitehead [Formula: see text]-duality, which is defined on the category of [Formula: see text]-algebras whose [Formula: see text]-theory is finitely generated and that satisfy the UCT, with morphisms the [Formula: see text]-groups. We explore what happens when these assumptions are relaxed in various ways. In particular, we consider the relationship between Paschke duality and Spanier–Whitehead [Formula: see text]-duality.