A C*-algebra of geometric operators on self-similar CW-complexes. Novikov-Shubin and L2-Betti numbers
Fabio Cipriani, Daniele Guido, Tommaso Isola
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 Deltaj 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-Poincare' characteristic is proved. L2-Betti and Novikov-Shubin numbers are computed for some self-similar complexes arising from self-similar fractals.
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