2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/214411A 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.30 pages, 7 figuresOperator AlgebrasAlgebraic TopologyCombinatorics58J50, 46Lxx, 57-xx, 57M15text