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

IF 1.1 4区 数学 Q1 MATHEMATICS
T. Maruyama, Tatsuki Seto
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引用次数: 1

Abstract

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.
基于$n$-立方体的自相似集上的组合Fredholm模
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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来源期刊
CiteScore
1.50
自引率
0.00%
发文量
9
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