Cyclic Cohomology Groups of Some Self-similar Sets

Takashi Maruyama

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arXiv · 1612.03311

Cyclic Cohomology Groups of Some Self-similar Sets

Takashi Maruyama

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Abstract

We define a variant of the Young integration on some kinds of self-similar sets which are called cellular self-similar sets. This variant is an analogue of the Young integration defined on the unit interval. We give the criteria of the variant on cellular self-similar sets, and also show that the variant is a cyclic 1-cocycle of the algebra of complex-valued H\"older continuous functions on the cellular self-similar sets. This suggests that the cocycle is a variant of currents.

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Takashi Maruyama. 2016-12-10. Cyclic Cohomology Groups of Some Self-similar Sets. https://arxiv.org/abs/1612.03311

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