TOPOLOGICAL OBSTRUCTIONS TO BRST INVARIANCE

It is shown that, due to topological obstructions, the effective actio n of a gauge theory in a multiple-connected space-time containing one fermion n-plet in the fundamental representation of the covering group of the gauge group is not, in general, BRST-invariant. A resolution t o this problem is attained with the introduction of identical copies o f the original n-plet, one for each of the effectively independent com ponents of the symmetry group, and a truly invariant generating functi onal is constructed. Examples with explicit gauge groups and their pos sible relevance to the family problem or to the SU(3) flavors of quark s are briefly discussed.