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Journal of Operator Theory

Volume 68, Issue 2, Fall 2012  pp. 567-596.

The entire cyclic cohomology of noncommutative $3$-spheres

Authors Katsutoshi Kawashima (1) and Hiroshi Takai (2)
Author institution: (1) Department of Liberal Arts, Kurume National College of Technology, Kurume, Fukuoka, 830--8555, Japan
(2) Mathematics and Information Science, Tokyo Metropolitan University, Hachioji, Tokyo, 192-0397, Japan

Summary:  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 Fr\'echet $*$-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.

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