Topological invariants of time reversal invariant superconductors

The topological invariants of gapped time reversal invariant lattice superconductors are studied by mapping the superconducting mean field Hamiltonian to a Bloch Hamiltonian. There is a single $Z_2$ invariant in two dimensions and four such invariants in three dimensions. We briefly discuss the properties of states with non-trivial topological invariants.