In this paper we give a proof of the Gauss–Bonnet theorem of Connes and Tretkoff for noncommutative two tori equipped with an arbitrary translation invariant complex structure. More precisely, we show that for any complex number in the upper half plane, representing the conformal class of a metric on , and a Weyl factor given by a positive invertible element , the value at the origin, , of the spectral zeta function of the Laplacian attached to is independent of and .
Cite this article
Farzad Fathizadeh, Masoud Khalkhali, The Gauss–Bonnet theorem for noncommutative two tori with a general conformal structure. J. Noncommut. Geom. 6 (2012), no. 3, pp. 457–480DOI 10.4171/JNCG/97