We represent the ℤ₂ topological invariant characterizing a one-dimensional topological superconductor using a WessZuminoWitten dimensional extension. The invariant is formulated in terms of the single-particle Greens function which allows us 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 Greens 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.