Cyclic Cohomology Groups of Some Self-similar Sets

Takashi Maruyama

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Cyclic Cohomology Groups of Some Self-similar Sets

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arxiv 1612.03311 v1 pith:GBBEC6VR submitted 2016-12-10 math.MG math.ATmath.CA

Cyclic Cohomology Groups of Some Self-similar Sets

Takashi Maruyama This is my paper

classification math.MG math.ATmath.CA

keywords self-similarsetsvariantcellularcocyclecyclicintegrationsome

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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.

Cyclic Cohomology Groups of Some Self-similar Sets

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