Abstract
The existence of Gribov ambiguities in SU(m)×U(1) gauge theories over the n-spheres is discussed herein. The goal of this article is achieved 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 SU(m)×U(1) fiber bundles over the n-spheres. By using properties of the space of maps Map*(Sn,G) where G is one of U(1), SU(m), we are able to determine the homotopy type of the groups of gauge transformations in terms of the homotopy groups of G. The nontriviality of these homotopy groups gives the desired result.
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