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The aim of the present work is to show how, using the differential calculusassociated to Dirichlet forms, it is possible to construct Fredholm modules onpost critically finite fractals by regular harmonic structures. The modules ared-summable, the summability exponent d coinciding with the spectral dimensionof the generalized laplacian operator associated with the regular harmonicstructures. The characteristic tools of the noncommutative infinitesimalcalculus allow to define a d-energy functional which is shown to be aself-similar conformal invariant.

Fredholm Modules on P.C.F. Self-Similar Fractals and their Conformal Geometry