Abstract
Our understanding of the local index formula in noncommutative geometry has stalled for a while because we do not have more than one explicit computation, namely that of Connes for quantum SU(2), and we do not understand the meaning of the various multilinear functionals involved in the formula. In such a situation further progress in understanding necessitates more explicit computations, and here we execute the second explicit computation for the quantum double suspension, a construction inspired by the Toeplitz extension. More specifically, we compute the local index formula for the quantum double suspensions of $$C(\mathcal {S}^2)$$ and the noncommutative 2-torus.
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