Spectral triples and the geometry of fractals
Operator Algebras
2011-09-22 v2 K-Theory and Homology
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.
Keywords
Cite
@article{arxiv.1002.3081,
title = {Spectral triples and the geometry of fractals},
author = {Erik Christensen and Cristina Ivan and Elmar Schrohe},
journal= {arXiv preprint arXiv:1002.3081},
year = {2011}
}
Comments
29 pages, 9 figures, The title in the first version was: "On the choice of a spectral triple". The title and parts of the manuscript have been changed in accordance with suggetions made by the referee. The article will appear in Journal of noncommutative geometry