Topological superfluids with time reversal symmetry

It is shown that superfluids in two and three dimensions which have time reversal invariant ground states have phases which are distinguished by a topological invariant. Further, it is shown that the B-phase of $^3$ He is a superfluid in the non-trivial topological class. Superfluids in the non-trivial topological class are shown to have gapless edge states and support various kinds of vortices with zero energy modes localized in their cores. Some of these vortices have non-abelian statistics.