arXiv subjects

Katsutoshi Naito

Publications and source records attributed to Katsutoshi Naito.

2 recordsLinked to original sources

arXiv2010

The Entire Cyclic Cohomology of Noncommutative 2-Tori

Our aim in this paper is to compute the entire cyclic cohomology of noncommutative 2-tori. First of all, we clarify their algebraic structure of noncommutative 2-tori as a $F^*$-algebra, according to the idea of Elliott-Evans. Actually, they are the inductive limit of subhomogeneous $F^*$-algebras. Using such a result, we compute their entire cyclic cohomology, which is isomorphic to their periodic one as a complex vector space.

math.KT↗

arXiv2010

The Entire Cyclic Cohomology of Noncommutative 3-Spheres

In this paper, we compute the entire cyclic cohomology of noncommutative 3-spheres. First of all, we verify the Mayer-Vietoris exact sequence of entire cyclic cohomology in the framework of Fréchet $^*$-algebras. Applying it to their noncommutative Heegaard decomposition, we deduce that their entire cyclic cohomology is isomorphic to the d'Rham homology of the ordinary 3-sphere with the complex coefficients.

math.KT↗