Understand
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.
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