A combinatorial Fredholm module on self-similar sets built on $n$-cubes

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.

31 pages, to appear in J. Fractal Geom