3 papers
math.KT2022
A combinatorial integration on the Cantor dust
Takashi Maruyama, Tatsuki Seto
In this paper, we generalize the Cantor function to -dimensional cubes and construct a cyclic -cocycle on the Cantor dust. This cocycle is non-trivial on the pullback of the…
math.KT2019
A combinatorial Fredholm module on self-similar sets built on -cubes
Takashi Maruyama, Tatsuki Seto
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 Conne…
math.MG2016
Cyclic Cohomology Groups of Some Self-similar Sets
Takashi Maruyama
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 de…