  We develop a theory for interacting fermions in the presence of spin-orbit
coupling and Zeeman fields, and show that many new superfluids phases, which
are topological in nature, emerge. Depending on values of spin-orbit coupling,
Zeeman fields, and interactions, initially gapped s-wave superfluids acquire
p-wave, d-wave, f-wave and higher angular momentum components, which produce
zeros in the excitation spectrum, rendering the superfluid gapless. Several
multi-critical points, which separate topological superfluid phases from normal
or non-uniform, are accessible depending on spin-orbit coupling, Zeeman fields
or interactions, setting the stage for the study of tunable topological
superfluids.
