Mathematics

I will give examples of noncommutative self-coverings, and describe how a spectral triple on the base space can be extended to a spectral triple on the inductive family of coverings, in such a way that the covering projections are locally isometric. I will show that such triples converge, in a suitable sense, to a semifinite spectral triple on the direct limit of the tower of coverings, which I call noncommutative solenoidal space. Some of the self-coverings described are given by the inclusion of the fixed point algebra in a C∗-algebra acted upon by a finite abelian group. In all the examples treated, the noncommutative solenoidal spaces have the same metric dimension and volume as  the base space, while the pseudo-metric induced by the spectral triple does not produce the weak∗topology on the state space