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In this paper we give a proof of the Gauss-Bonnet theorem of Connes and Tretkoff for noncommutative two tori $\mathbb{T}_{\theta}^2$ equipped with an arbitrary translation invariant complex structure.
A. Connes, C ∗ C^{*} -algèbres et géométrie différentielle
1980
Earlier work this paper cites.
P. Gilkey, Invariance theory, the heat equation, and the Atiyah-Singer index theorem
1984
Earlier work this paper cites.
S. Baaj, Calcul pseudo-différentiel et produits croisés de C ∗ C^{*} -algèbres
1988
Earlier work this paper cites.
A. Connes, Noncommutative geometry
1994
Cited alongside, same era.
A. Chamseddine, A. Connes, The Spectral action principle
1997
Cited alongside, same era.
P. B. Cohen and A. Connes, Conformal geometry of the irrational rotation algebra
Cited in the paper.
A. Connes, H. Moscovici, Type III and spectral triples
Cited in the paper.
A. Connes and P. Tretkoff, The Gauss-Bonnet theorem for the noncommutative two torus
Cited in the paper.
S. Rosenberg, The Laplacian on a Riemannian manifold
1997
Later among the works it cites.
A. Chamseddine, A. Connes, Scale invariance in the spectral action
2006
Later among the works it cites.
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