  We report intimate relations between topological properties of full gapped
spin-triplet superconductors with time-reversal invariance and the Fermi
surface topology in the normal states. An efficient method to calculate the Z2
invariants and the winding number for the spin-triplet superconductors is
developed, and connections between these topological invariants and the Fermi
surface structures in the normal states are pointed out. We also obtain a
correspondence between the Fermi surface topology and gapless surface states in
the superconducting states. The correspondence is inherent to spin-triplet
superconductivity.
