CodiceQDD 119
TitoloSpectral Triples for the Sierpinski gasket
Autore/iCipriani, F.; Guido, D. Isola, T. Sauvageot J.L.
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AbstractWe construct a 2-parameter family of spectral triples for the Sierpinski Gasket K. We determine their associated Connes distances in terms of suitable roots of the plane Euclidean metric and their dimensional spectra, and show that the pairing of the associated Fredholm module with (odd) K-theory is non-trivial. We recover the Hausdorff measure of K in terms of the residue of a functional at its abscissa of convergence d, which coincides with the Hausdorff dimension of the fractal. We recover also the unique, standard Dirichlet form on K, as the residue of another functional at its abscissa of convergence d , which we call the energy dimension. The fact that the volume dimension diff ers from the energy dimension reflects the fact that on K energy and volume are distributed singularly.