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 $\mathbf{Z}$. 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.

arXiv comment16 pages, AMS Latex, uses package diagrams