  In this letter, we investigate topological phases of full-gapped odd-parity
superconductors, which are distinguished by the bulk topological invariants and
the topologically protected gapless boundary states. Using the particle-hole
symmetry, we introduce Z_2 invariants characterizing topological odd-parity
superconductors without or with time-reversal invariance. For odd-parity
superconductors, a combination of the inversion and the U(1) gauge symmetry is
manifestly preserved, and the combined symmetry enables us to evaluate the Z_2
invariants from the knowledge of the Fermi surface structure. Relating the Z_2
invariants to other topological invariants, we establish characterization of
topological odd-parity superconductors in terms of the Fermi surface topology.
Simple criteria for topological odd-parity superconductors in various
dimensions are provided. Implications of our formulas for nodal odd-parity
superconductors are also discussed.
