自相似CW-复形上几何算子的C* 代数。Novikov-Shubin数与L^2-贝蒂数
A C*-algebra of geometric operators on self-similar CW-complexes. Novikov-Shubin and L^2-Betti numbers
摘要：
引入了一类CW-复形，称为自相似复形，以及作用于平方可和胞腔j-链上的具有有限迹的算子的C* 代数Aj.由于Laplacian Delta_j属于A_j，因此我们定义了这类复形的L^2-贝蒂数和Novikov-Shubin数.特别是一个关系，涉及Euler-Poincare的特征证明。计算了由自相似分形产生的自相似复体的L^2-Betti数和Novikov-Shubin数。
英文摘要：
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.
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