SpanierWhitehead $K$duality
SpanierWhitehead $K$duality

Claude Schochet, Technion University
Fine Hall 322
Classical SpanierWhitehead duality was introduced for the stable homotopy category of finite CW complexes. We consider a noncommutative version, termed SpanierWhitehead $K$duality, which is defined on the category of $C^*$algebras whose $K$theory is finitely generated and that satisfy the UCT, with morphisms the Kasparov $KK$groups. Examples from foliations, hyperbolic dynamics, and other highly noncommutative $C^*$algebras illustrate the truly new phenomena encountered. There are many open questions associated with relaxing the assumptions on the algebras. For example, does the Calkin algebra have a SpanierWhitehead $K$dual? This is joint work with JerryKaminker.