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 Delta j belongs to Aj. 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. (C) 2008 Elsevier Inc. All rights reserved.

Cipriani, F., Guido, D., Isola, T. (2009). A C*-algebra of geometric operators on self-similar CW-complexes. Novikov-Shubin and L-2-Betti numbers. JOURNAL OF FUNCTIONAL ANALYSIS, 256(3), 603-634 [10.1016/j.jfa.2008.10.013].

A C*-algebra of geometric operators on self-similar CW-complexes. Novikov-Shubin and L-2-Betti numbers

GUIDO, DANIELE;ISOLA, TOMMASO
2009-02-01

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 Delta j belongs to Aj. 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. (C) 2008 Elsevier Inc. All rights reserved.
feb-2009
Pubblicato
Rilevanza internazionale
Articolo
Sì, ma tipo non specificato
Settore MAT/05 - ANALISI MATEMATICA
English
Con Impact Factor ISI
Fractal graphs; Geometric operators; Homological Laplacians; L2-invariants; Self-similar CW-complexes; Traces on amenable spaces
Cipriani, F., Guido, D., Isola, T. (2009). A C*-algebra of geometric operators on self-similar CW-complexes. Novikov-Shubin and L-2-Betti numbers. JOURNAL OF FUNCTIONAL ANALYSIS, 256(3), 603-634 [10.1016/j.jfa.2008.10.013].
Cipriani, F; Guido, D; Isola, T
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/2108/25628
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