Abstract :
We establish six terms exact sequences relating the KK-theory groups and the E-theory groups of an amalgamated free product C∗-algebra, A1∗BA2, to the respective groups of the three constituents, A1,A2 and B. In the KK-theory case, we assume that B is finite dimensional, but in the E-theory case only that B is nuclear, or is the range of a conditional expectation in both A1 and A2. In particular, we obtain the conjectured six terms exact sequence for the K-theory of an amalgamated free product in this generality.
