  We calculate the effective three-body force for bosons interacting with each
other by a two-body potential tuned to a narrow zero crossing in any dimension.
We use the standard two-channel model parametrized by the background atom-atom
interaction strength, the amplitude of the open-channel to closed-channel
coupling, and the atom-dimer interaction strength. The three-body force
originates from the atom-dimer interaction, but it can be dramatically enhanced
for narrow crossings, i.e., for small atom-dimer conversion amplitudes. This
effect can be used to stabilize quasi-two-dimensional dipolar atoms and
molecules.
