Spectral triples for noncommutative solenoidal spaces from self-coverings

Tommaso Isola
Roma "Tor Vergata"
Wednesday, June 22, 2016 - 16:00

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.

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