Cyclic Cohomology Groups of Some Self-similar Sets
Metric Geometry
2016-12-19 v1 Algebraic Topology
Classical Analysis and ODEs
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.
Keywords
Cite
@article{arxiv.1612.03311,
title = {Cyclic Cohomology Groups of Some Self-similar Sets},
author = {Takashi Maruyama},
journal= {arXiv preprint arXiv:1612.03311},
year = {2016}
}
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26 pages