Abstract
Given a spectral triple ( A , H , D ) Connes associated a canonical differential graded algebra Ω D • ( 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 Ω D • for spectral triples obtained by iterated quantum 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.
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