Dirac operators and geodesic metric on the harmonic Sierpinski gasket and other fractal sets

@article{Lapidus2014DiracOA,
  title={Dirac operators and geodesic metric on the harmonic Sierpinski gasket and other fractal sets},
  author={Michel L. Lapidus and Jonathan J. Sarhad},
  journal={Journal of Noncommutative Geometry},
  year={2014},
  volume={8},
  pages={947-985}
}
We construct Dirac operators and spectral triples for certain, not necessarily self-similar, fractal sets built on curves. Connes' distance formula of noncommutative geometry provides a natural metric on the fractal. To motivate the construction, we address Kigami's measurable Riemannian geometry, which is a metric realization of the Sierpinski gasket as a self-affine space with continuously differentiable geodesics. As a fractal analog of Connes' theorem for a compact Riemmanian manifold, it… 
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