We give a superconnection proof of Connes’ index theorem for proper cocompact actions of étale groupoids. This includes Connes’ general foliation index theorem for foliations with Hausdor¤ holonomy groupoid.

Abstract We show that the universal minimal proximal flow and strongly of a discrete group can be realized as Stone spaces translation-invariant Boolean algebras subsets satisfying higher-order notion syndeticity. establish algebraic, combinatorial topological dynamical characterizations these we use to obtain new necessary sufficient conditions for strong amenability amenability. also characte...

Let Lω(G) be a Beurling algebra on a locally compact abelian group G. We look for general conditions on the weight which allows the vanishing of continuous derivations of Lω(G). This leads us to introducing vector-valued Beurling algebras and considering the translation of operators on them. This is then used to connect the augmentation ideal to the behavior of derivation space. We apply these ...