NCG seminar

[Emanuele Tuillier Illingworth]

NCG Seminar

Prof. Tommaso Isola (Roma "Tor Vergata")

"Spectral triples for noncommutative solenoidal spaces from self-coverings"

Abstract:
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.

SISSA, room 136, Wed. 22 June 2016, 4 pm