Trieste, August 26-28 2014

K-homology and graph algebras

Fredholm modules over graph C*-algebras

The K-homology of a graph C*-algebra can be identified with the kernel and cokernel of a certain integer matrix associated to the graph. This result has been proved several times, in varying degrees of generality, beginning with Cuntz and Krieger. The isomorphisms from K-homology to the combinatorially-defined homology groups are given by simple index formulas, which make it a relatively easy matter to write down explicit Fredholm modules representing any K-homology class, or to check whether two Fredholm modules determine the same class. I will illustrate with some computations for "quantum" projective spaces and lens spaces.