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

Takashi Maruyama; Tatsuki Seto

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

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arxiv 1912.05832 v4 pith:LOQKUXYQ submitted 2019-12-12 math.KT math.DGmath.MG

Takashi Maruyama , Tatsuki Seto This is my paper · ORCID

classification math.KTmath.DGmath.MG

keywords fredholmmodulecantorcombinatorialconstructionself-similarsetsanalogue

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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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