| Résume | Coarse geometry is the study of metric spaces when one forgets about the small scale structure and focuses only on large scales. Objects and maps of interest are coarse spaces and coarse equivalences. Typical examples important for applications are finitely generated groups with word metrics, and discretisations of non-discrete spaces such as Riemannian manifolds. To a coarse space one associates, after Roe, several C*-algebras capable of detecting algebraically the geometric properties of the space. Chief among these, for applications, is the uniform Roe algebra of X, C_u*(X). We show that if X and Y are uniformly locally finite spaces whose uniform Roe algebras are isomorphic, then X and Y are coarsely equivalent. This is joint work with Baudier, Braga, Farah, Khukhro and Willett. |
