  I show that two-dimensional nematic order in an active fluid film can be
stable and long-ranged if exchange of particles and momentum with an ambient
three-dimensional fluid is allowed. Number-conserving films present an
instability, with a fastest-growing mode independent of activity at high
activities or low concentrations. Motility can stabilize long-range polar order
on such immersed surfaces even when the swimmer number in the film is
conserved. Active ordering in immersed surfaces is much richer than previously
expected, with functional consequences for active transport, and suggests that
a broader exploration of parameters in current and future experiments would
display the new features predicted here.
