  We show that time-reversal invariant superconductors in d=2 (d=3) dimensions
can support topologically stable Fermi points (lines), characterized by an
integer topological charge. Combining this with the momentum space symmetries
present, we prove analogs of the fermion doubling theorem: for d=2 lattice
models admitting a spin X electron-hole structure, the number of Fermi points
is a multiple of four, while for d=3, Fermi lines come in pairs. We show two
implications of our findings for topological superconductors in d=3: first, we
relate the bulk topological invariant to a topological number for the surface
Fermi points in the form of an index theorem. Second, we show that the
existence of topologically stable Fermi lines results in extended gapless
regions in a generic topological superconductor phase diagram.

Superconductivity