Fredholm modules over certain group C*-algebras

Abstract

Motivated by the search for new examples of "noncommutative manifolds", we study the noncommutative geometry of the group C*-algebras of various discrete groups. The examples we consier are the infinite dihedral group ${\bf Z} \times_{\sigma} {\bf Z}_2$ and the semidirect product ${\bf Z} \times_{\sigma} {\bf Z}$. We present a unified treatment of the K-homology and cyclic cohomology of these algebras.