## A C∗-algebra of geometric operators on self-similar CW-complexes. Novikov–Shubin and L²-Betti numbers (2006)

by
Fabio Cipriani
,
Daniele Guido
,
Tommaso Isola

Citations: | 2 - 2 self |

### BibTeX

@MISC{Cipriani06ac∗-algebra,

author = {Fabio Cipriani and Daniele Guido and Tommaso Isola},

title = {A C∗-algebra of geometric operators on self-similar CW-complexes. Novikov–Shubin and L²-Betti numbers },

year = {2006}

}

### OpenURL

### Abstract

A class of CW-complexes, called self-similar complexes, is introduced, together with C∗-algebras Aj of operators, endowed with a finite trace, acting on square-summable cellular j-chains. Since the Laplacian ∆j belongs to Aj, L²-Betti numbers and Novikov-Shubin numbers are defined for such complexes in terms of the trace. In particular a relation involving the Euler-Poincaré characteristic is proved. L²-Betti and Novikov-Shubin numbers are computed for some self-similar complexes arising from self-similar fractals.