  We discuss the emergence of rings of zero-energy excitations in momentum
space for superfluid phases of ultra-cold fermions when spin-orbit, Zeeman
fields and interactions are varied. We show that phases containing rings of
nodes possess non-trivial topological invariants, and that phase transitions
between distinct topological phases belong to the Lifshitz class. Upon crossing
phase boundaries, existing massless Dirac fermions in the gapless phase
anihilate to produce bulk zero-mode Majorana fermions at phase boundaries and
then become massive Dirac fermions in the gapped phase. We characterize these
tunable topological phase transitions via several spectroscopic properties,
including excitation spectrum, spectral function and momentum distribution.
Since the emergence or disappearance of rings leads to topological transitions
in momentum space, we conclude that Lifshitz is the lord of the rings.
