Séminaires : Séminaire d'Analyse Fonctionnelle

In the late 80s John Roe defined a family of C*-algebras capable of detecting coarse geometric properties of metric spaces in operator algebraic terms; these are called Roe-like algebras. It is fairly elementary to show that if two metric spaces look the same in coarse geometric terms, that is, if they are (bijectively) coarsely equivalent, then the associated Roe-like algebras are isomorphic. In this talk, we investigate the converse implications, trying to extract geometric information from algebraic data.