COMMENTS ON THE GRIBOV AMBIGUITY

The existence of Gribov ambiguities in SU(m) X U(1) gauge theories ove r the n-spheres is discussed herein. The goal of this article is achie ved by showing that there is exactly one conjugacy class of groups of gauge transformations for the theories given above. This implies that these transformation groups are conjugate to the ones of the trivial S U(m) X U(1) fiber bundles over the n-spheres. By using properties of t he space of maps Map(S(n), G) where G is one of U(1), SU(m), we are a ble to determine the homotopy type of the groups of gauge transformati ons in terms of the homotopy groups of G. The nontriviality of these h omotopy groups gives the desired result.