Spectral triples and quantum statistical mechanical systems are two important constructions in noncommutative geometry. In particular, both lead to interesting reconstruction theorems for a broad range of geometric objects, including number fields, spin manifolds, graphs. There are similarities between the two structures, and we show that the notion of type III σspectral triple, introduced rece...

Noncommutative geometric gauge theory is reconstructed based on the superconnection concept. The bosonic action of the Connes-Lott model including the symmetry breaking Higgs sector is obtained by using a new generalized derivative, which consists of the usual 1-form exterior derivative plus an extra element called the matrix derivative, for the curvatures. We first derive the matrix derivative...

Differential structure of a d-dimensional lattice, which is essentially a noncommutative exterior algebra, is defined using reductions in first order and second order of universal differential calculus in the context of noncommutative geometry(NCG) developed by Dimakis et al. This differential structure can be realized adopting a Dirac-Connes operator proposed by us recently within Connes’ NCG....

We consider an $\ell^p$ coarse Baum-Connes assembly map for $1<p<\infty$, and show that it is not surjective expanders arising from residually finite hyperbolic groups.