Abstract
We study countable sums of two dimensional modules for the continuous complex functions on a compact metric space and show that it is possible to construct a spectral triple which gives the original metric back. This spectral triple will be finitely summable for any positive parameter. We also construct a sum of two dimensional modules which reflects some aspects of the topological dimensions of the compact metric space, but this will only give the metric back approximately. At the end we make an explicit computation of the last module for the unit interval in. The metric is recovered exactly, the Dixmier trace induces a multiple of the Lebesgue integral but the growth of the number of eigenvalues is different from the one found for the standard differential operator on the unit interval.
| Original language | English |
|---|---|
| Journal | Mathematica Scandinavica |
| Volume | 100 |
| Issue number | 1 |
| Pages (from-to) | 35-60 |
| Number of pages | 26 |
| ISSN | 0025-5521 |
| Publication status | Published - 2007 |
Keywords
- Faculty of Science
- mathematics
- non commutative geometry