Given a spectral triple $(\mathcal{ A},\mathcal{ H},D)\,$ Connes associated a canonical differential graded algebra $\,\Omega_D^\bullet(\mathcal{ A})$. However, so far this has been computed for very few special cases. We identify suitable hypotheses on a spectral triple that helps one to compute the associated Connes' calculus for its quantum double suspension. This allows one to compute $\,\Omega_D^\bullet$ for spectral triples obtained by iterated quatum double suspension of the spectral triple associated with a first order differential operator on a compact smooth manifold. This gives the first systematic computation of Connes' calculus for a large family of spectral triples.
Categories: math.QA math.OA