  A time reversal invariant (TRI) topological superconductor has a full pairing
gap in the bulk and topologically protected gapless states on the surface or at
the edge. In this paper, we show that in the weak pairing limit, the
topological quantum number of a TRI superconductor can be completely determined
by the Fermi surface properties, and is independent of the electronic structure
away from the Fermi surface. In three dimensions (3D), the integer topological
quantum number in a TRI superconductor is determined by the sign of the pairing
order parameter and the first Chern number of the Berry phase gauge field on
the Fermi surfaces. In two (2D) and one (1D) dimension, the $Z_2$ topological
quantum number of a TRI superconductor is determined simply by the sign of the
pairing order parameter on the Fermi surfaces. We also obtain a generic and
explicit expression of the $Z_2$ topological invariant in 1D and 2D.
