An Asymmetric Noncommutative Torus

Abstract

We introduce a family of spectral triples that describe the curved noncommutative two-torus. The relevant family of new Dirac operators is given by rescaling one of two terms in the flat Dirac operator. We compute the dressed scalar curvature and show that the Gauss-Bonnet theorem holds (which is not covered by the general result of Connes and Moscovici).

References in corpus (5)

• Type III and spectral triples
• The Gauss-Bonnet Theorem for the noncommutative two torus
• Levi-Civita's Theorem for Noncommutative Tori
• Curved noncommutative torus and Gauss--Bonnet
• Noncommutative Geometry and Conformal Geometry. III. Vafa-Witten Inequality and Poincaré Duality

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• Einstein-Hilbert Action and on the Gauss-Bonnet Theorem for Riemannian Noncommutative Tori