Apparaît dans la collection : Group operator algebras and Non commutative geometry / Algèbres d'opérateurs de groupes et Geometrie non commutative

For a class of fundamental groups of closed oriented hyperbolic 3-manifolds acting on their Gromov boundary, we compute the K-theory of the associated crossed products in terms of the first homology group of the manifold. Using classification results of purely infinite C*-algebras, we conclude that there exist infinitely many pairwise nonisomorphic torsion-free hyperbolic groups acting on their boundary, for which all crossed products are isomorphic. As in all these cases the boundary is homeomorphic to the 2-sphere, we find infinitely many pairwise non-conjugate Cartan subalgebras with spectrum $S^2$ in such crossed products. This is joint work with Johannes Ebert and Julian Kranz.