Noncommutative Geometry Seminar

Noncommutative 2-torus is one of the main toy-models of

noncommutative geometry, and noncommutative n-torus is a straightforward

generalization of it. In 1980 Pimsner and Voiculescu described a 6-term

exact sequence, which allows to compute the K-theory of non-commutative

tori. It follows, that both even and odd K-groups of n-dimensional

noncommutative tori are free abelian groups on 2^(n-1) generators. The

first non-trivial generator is the one of the even K-theory of the

noncommutative 2-torus. It is known from 1981 as the Powers-Rieffel

projector. The next one is a generator of the odd K-theory of the

noncommutative 3-torus. The goal of this talk is to describe it

explicitly.