A combinatorial Fredholm module on self-similar sets built on $n$-cubes
K-Theory and Homology
2023-04-05 v4 Differential Geometry
Metric Geometry
Abstract
We construct a Fredholm module on self-similar sets such as the Cantor dust, the Sierpinski carpet and the Menger sponge. Our construction is a higher dimensional analogue of Connes' combinatorial construction of the Fredholm module on the Cantor set. We also calculate the Dixmier trace of two operators induced by the Fredholm module.
Cite
@article{arxiv.1912.05832,
title = {A combinatorial Fredholm module on self-similar sets built on $n$-cubes},
author = {Takashi Maruyama and Tatsuki Seto},
journal= {arXiv preprint arXiv:1912.05832},
year = {2023}
}
Comments
31 pages, to appear in J. Fractal Geom