  In this paper we introduce four Z_2 topological indices zeta_k=0,1 at
k=(0,0), (0,pi), (pi, 0), (pi, pi) characterizing 16 universal classes of 2D
superconducting states that have translation symmetry but may break any other
symmetries. The 16 classes of superconducting states are distinguished by their
even/odd numbers of fermions on even-by-even, even-by-odd, odd-by-even, and
odd-by-odd lattices. As a result, the 16 classes topological superconducting
states exist even for interacting systems. For non-interacting systems, we find
that zeta_k is the number of electrons on k=(0,0), (0,pi), (pi, 0), or (pi,pi)
orbitals (mod 2) in the ground state. For 3D superconducting states with only
translation symmetry, there are 256 different types of topological
superconductors.
