Fredholm modules over graph C*-algebras

TL;DR

This paper applies explicit formulas to compute K-homology of graph C*-algebras, showing all classes can be represented by finite-rank commutator Fredholm modules and constructing generators for quantum lens spaces.

Contribution

It demonstrates that every K-homology class of graph C*-algebras has a finite-rank commutator Fredholm module and provides explicit generators for quantum lens spaces.

Findings

All K-homology classes are represented by finite-rank commutator Fredholm modules.

Explicit generating Fredholm modules for quantum lens spaces.

Application of Cuntz-Krieger formulas to K-homology computations.

Abstract

We present two applications of explicit formulas, due to Cuntz and Krieger, for computations in K-homology of graph C*-algebras. We prove that every K-homology class for such an algebra is represented by a Fredholm module having finite-rank commutators; and we exhibit generating Fredholm modules for the K-homology of quantum lens spaces.