An asymmetric noncommutative torus (Q887755)

The authors introduce a new class of spectral triples which describe differential geometry of the non-commutative torus. The associated Dirac operators are obtained through a rescaling of the flat Dirac operator by elements of the opposite coordinate algebra. It is proved that an analog of the Gauss-Bonnet theorem is valid for the new family of spectral triples. A draft of the paper is available at \texttt{http://arxiv.org/abs/1406.4645}.