Deformations of wreath products

Abstract

Connectivity is a homotopy invariant property of a separable C ∗ -algebra A, which has three important consequences: absence of nontrivial projections, quasidiagonality and realization of the Kasparov group K K ( A , B ) as homotopy classes of asymptotic morphisms from A to B ⊗ K if A is nuclear. Here we give a new characterization of connectivity for separable exact C*-algebras and use this characterization to show that the class of discrete countable amenable groups whose augmentation ideals are connective is closed under generalized wreath products. In a related circle of ideas, we give a result on quasidiagonality of reduced crossed-product C*-algebras associated to noncommutative Bernoulli actions.