Codice  QDD 119 
Titolo  Spectral Triples for the Sierpinski gasket 
Data  20120131 
Autore/i  Cipriani, F.; Guido, D. Isola, T. Sauvageot J.L. 
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Abstract  We construct a 2parameter 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) Ktheory is nontrivial. 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 differs from the energy dimension
reflects the fact that on K energy and volume are distributed singularly. 
