K-homology of the rotation algebras $A_{\theta}$

Abstract

We study the K-homology of the rotation algebras $A_{\theta}$ using the six term cyclic sequence for the K-homology of a crossed product by ${\bf Z}$. In the case where $\theta$ is irrational we use Pimsner and Voiculescu's work on AF-embeddings of the $A_{\theta}$ to search for the missing generator of the even K-homology.