  We represent the $\mathbb Z_2$~topological invariant characterizing a one
dimensional topological superconductor using a Wess-Zumino-Witten dimensional
extension. The invariant is formulated in terms of the single particle Green's
function which allows to classify interacting systems. Employing a recently
proposed generalized Berry curvature method, the topological invariant is
represented independent of the extra dimension requiring only the single
particle Green's function at zero frequency of the interacting system.
Furthermore, a modified twisted boundary conditions approach is used to
rigorously define the topological invariant for disordered interacting systems.
