基于$n$-立方体的自相似集上的组合Fredholm模

IF 1.1 4区数学 Q1 MATHEMATICS

Journal of Fractal Geometry Pub Date : 2019-12-12 DOI:10.4171/jfg/132

T. Maruyama, Tatsuki Seto

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引用次数: 1

摘要

我们在自相似集(如康托尘、谢尔宾斯基地毯和门格尔海绵)上构造了一个Fredholm模块。我们的构造是Connes在康托集上的Fredholm模块的组合构造的高维模拟。我们还计算了由Fredholm模引起的两个算子的Dixmier迹。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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A combinatorial Fredholm module on self-similar sets built on $n$-cubes

We construct a Fredholm module on self-similar sets such as the Cantor dust, the Sierpinski carpet and the Menger sponge. Our construction is a higher dimensional analogue of Connes' combinatorial construction of the Fredholm module on the Cantor set. We also calculate the Dixmier trace of two operators induced by the Fredholm module.

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来源期刊

Journal of Fractal Geometry MATHEMATICS-

CiteScore

1.50

自引率

0.00%

发文量