The Gauss-bonnet Theorem for the Noncommutative Two Torus

@inproceedings{Connes2009TheGT,
  title={The Gauss-bonnet Theorem for the Noncommutative Two Torus},
  author={Alain Connes and Paula Tretkoff},
  year={2009}
}
In this paper we shall show that the value at the origin, ζ(0), of the zeta function of the Laplacian on the non-commutative two torus, endowed with its canonical conformal structure, is independent of the choice of the volume element (Weyl factor) given by a (non-unimodular) state. We had obtained, in the late eighties, in an unpublished computation, a general formula for ζ(0) involving modified logarithms of the modular operator of the state. We give here the detailed computation and prove… CONTINUE READING

From This Paper

Figures, tables, and topics from this paper.

Explore Further: Topics Discussed in This Paper

References

Publications referenced by this paper.
Showing 1-10 of 11 references

Quasi homomorphismes, cohomologie cyclique et positivité

A Connes, J Cuntz
Comm. Math. Phys • 1988
View 1 Excerpt
Highly Influenced

Connes Conformal geometry of the irrational rotation algebra Preprint MPI

P B Cohen
Connes Conformal geometry of the irrational rotation algebra Preprint MPI
View 2 Excerpts
Highly Influenced

Type Iii and Spectral Triples

HENRI MOSCOVICI
2006
View 1 Excerpt

The Laplacian in a Riemannian manifold, LMS Student Texts 31, CUP

S Rosenberg
The Laplacian in a Riemannian manifold, LMS Student Texts 31, CUP • 1997
View 1 Excerpt

On the Non-commutative Torus of real dimension Two, Number Theory and Physics

P B Cohen
On the Non-commutative Torus of real dimension Two, Number Theory and Physics • 1990

Calcul pseudo-différentiel et produits croisés de C * -algèbres. I et II, C.R. Acad. Sc. Paris, t. 307, Série I

S Baaj
Calcul pseudo-différentiel et produits croisés de C * -algèbres. I et II, C.R. Acad. Sc. Paris, t. 307, Série I • 1988

C.R. Acad. Sc. Paris, t

A Connes, C *-Algèbres Et Géométrie Différentielle
C.R. Acad. Sc. Paris, t • 1980

Similar Papers

Loading similar papers…