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Tolerance relations and operator systems
Alain Connes, Walter D. van Suijlekom
We extend the scope of noncommutative geometry by generalizing the construction of the noncommutative algebra of a quotient space to situations in which one is no longer dealing wi…
Noncommutative Geometry for Symmetric Non-Self-Adjoint Operators
Alain Connes, Galina Levitina, Edward McDonald +2
We introduce the notion of a pre-spectral triple, which is a generalisation of a spectral triple where is no longer required to be self-adjoint, but close…
Trace theorem for quasi-Fuchsian groups
Alain Connes, Fedor Sukochev, Dmitriy Zanin
We complete the proof of the Trace Theorem in the quantized calculus for quasi-Fuchsian group which was stated and sketched, but not fully proved, on pp. 322-325 in the book "Nonco…
On the spectral characterization of manifolds
Alain Connes
We show that the first five of the axioms we had formulated on spectral triples suffice (in a slightly stronger form) to characterize the spectral triples associated to smooth comp…
Type III and spectral triples
Alain Connes, Henri Moscovici
We explain how a simple twisting of the notion of spectral triple allows to incorporate type III examples, such as those arising from the transverse geometry of codimension one fol…
KMS states and complex multiplication
Alain Connes, Matilde Marcolli, Niranjan Ramachandran
We construct a quantum statistical mechanical system which generalizes the Bost-Connes system to imaginary quadratic fields K of arbitrary class number and fully incorporates the e…