An Asymmetric Noncommutative Torus
Abstract
We introduce a family of spectral triples that describe the curved noncommutative twotorus. 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 GaussBonnet theorem holds (which is not covered by the general result of Connes and Moscovici).
 Publication:

SIGMA
 Pub Date:
 September 2015
 DOI:
 10.3842/SIGMA.2015.075
 arXiv:
 arXiv:1406.4645
 Bibcode:
 2015SIGMA..11..075D
 Keywords:

 noncommutative geometry;
 GaussBonnet;
 spectral triple;
 Mathematics  Quantum Algebra;
 Mathematical Physics;
 58B34;
 58J42
 EPrint:
 SIGMA 11 (2015), 075, 11 pages