  Static topologically-nontrivial configurations in sigma-models, for spatial
dimension D \geq 2, are unstable. The question addressed here is whether such
sigma-model solitons can be stabilized by steady rotation in internal space;
that is, rotation in a global SO(2) symmetry. This is the mechanism which
stabilizes Q-balls (non-topological solitons). The conclusion is that the
Q-mechanism can stabilize topological solitons in D=2 spatial dimensions, but
not for D=3.
