TOPOLOGICALLY STABLE LUMPS IN SO(D) GAUGED O(D-MODELS IN D DIMENSIONS- D=2, 3, 4(1) SIGMA)

The gauge-invariant topological charge is defined for, and the inequal ities supplying the lower bound on the action of an SO(4) gauged O(5) sigma model in four dimensions are established. The consistency of the solution with finiteness of the action and with topological stability is briefly verified for a particular dynamical example. Against the b ackground of the topologically stable finite energy solitons of SO(d) gauged O(d + 1) sigma models in d dimensions already known for d = 2 a nd for d = 3, the present example can be viewed as a demonstration by induction for the existence of such solitons in the case of arbitrary d.