The Chern-Simons action for perturbed Dirac triples

In \cite{PO1} and \cite{PO2}, Pfante defined a noncommutative Chern-Simons action for 3-summable spectral triples and computed the Chern-Simons action for ${\mathrm{S}\mathrm{U}}_q(2)$ and the noncommutative 3-torus. In this paper,we compute the Chern-Simons action for well-know perturbed Dirac triples.