Spectral triples and the geometry of fractals

Details Spectral triples and the geometry of fractals Spectral triples and the geometry of fractals

2010-02-16

arxiv.org/abs/1002.3081v2

Mathematics

Operator Algebras

29 pages, 9 figures, The title in the first version was: "On the choice of a spectral triple". The title and parts of the manu

Scientific paper

For each K-homolgy element of the Sierpinski gasket we construct a spectral triple which will generate that element. We show that there must be certain limits on the choice of the K-homology element if the geometric properties of the gasket shall be recoverable from that spectral triple. For a big subgroup of the K-homology group we show that our spectral triples will recover the metric, the dimension and the Hausdorff measure on the gaket.

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