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arXiv · 1002.3081

Spectral triples and the geometry of fractals

Erik Christensen·Cristina Ivan·Elmar Schrohe
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Abstract

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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Erik Christensen, Cristina Ivan, Elmar Schrohe. 2010-02-16. Spectral triples and the geometry of fractals. https://arxiv.org/abs/1002.3081

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