Abstract
We consider a wide class of 2D tight - binding models of solid state physics. These models are, in the most general case, non - homogeneous. The topological invariant N₃ responsible for the quantization of the Hall conductivity, for the specific case of the integer quantum Hall effect in 2D, is expressed through the Wigner transformation of the two-point electron Matsubara Green function. We express this invariant as a pairing of the element of the K⁻¹ group (generated by the Green function) with the specific element of the cyclic cohomology group HC³. According to a set of local index theorems the values of N₃ can be shown to be integer for a limited class of tight - binding models.