A C*-algebra of geometric operators on self-similar CW-complexes.   Novikov-Shubin and L^2-Betti numbers
  A class of CW-complexes, called self-similar complexes, is introduced, together with C*-algebras A_j of operators, endowed with a finite trace, acting on square-summable cellular j-chains. Since the Laplacian Delta_j belongs to A_j, L^2-Betti numbers and Novikov-Shubin numbers are defined for such complexes in terms of the trace. In particular a relation involving the Euler-Poincare' characteristic is proved. L^2-Betti and Novikov-Shubin numbers are computed for some self-similar complexes arising from self-similar fractals. 
Fabio Cipriani (Politecnico di Milano), Daniele Guido (U. Roma   TorVergata), Tommaso Isola (U. Roma TorVergata)