A combinatorial Fredholm module on self-similar sets built on \(n\)-cubes (Q6080842)
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scientific article; zbMATH DE number 7754868
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | A combinatorial Fredholm module on self-similar sets built on \(n\)-cubes |
scientific article; zbMATH DE number 7754868 |
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A combinatorial Fredholm module on self-similar sets built on \(n\)-cubes (English)
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25 October 2023
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Summary: We construct a Fredholm module on self-similar sets such as the Cantor dust, the Sierpiński 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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Fredholm module
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spectral triple
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self-similar set
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Hausdorff dimension
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