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.I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.
