| We investigate the status of the group C*-algebras of two discrete groups, the infinite dihedral and discrete Heisenberg groups, as “noncommutative differentiable manifolds” within the framework of Connes' noncommutative geometry. We study the K-homology, cyclic cohomology and derivations of these algebras, and consider some interesting generalizations.; Motivated by our study of the discrete Heisenberg group, we define and study a morphism from the K-homology of an algebra to the K-homology of its crossed product by an action of Z, dual to the Pimsner-Voiculescu sequence on K-theory. |
