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arXiv · 2209.03537

A combinatorial integration on the Cantor dust

Takashi Maruyama·Tatsuki Seto
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Abstract

In this paper, we generalize the Cantor function to $2$-dimensional cubes and construct a cyclic $2$-cocycle on the Cantor dust. This cocycle is non-trivial on the pullback of the smooth functions on the $2$-dimensional torus with the generalized Cantor function while it vanishes on the Lipschitz functions on the Cantor dust. The cocycle is calculated through the integration of $2$-forms on the torus by using a combinatorial Fredholm module.

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Takashi Maruyama, Tatsuki Seto. 2022-09-08. A combinatorial integration on the Cantor dust. https://arxiv.org/abs/2209.03537

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