Abstract
We show the existence of Gribov ambiguity for gauge group SU (N) and large classes of space-time manifolds with dimension less than or equal to four, working in the continuous category, extending previous results of Singer. In lower dimensions, and in four dimensions with gauge group SU (N), N≥3, we require only that the manifold be compact and orientable. In four dimensions with gauge group SU (2) there is a slight complification due to the fact that π4( SU (2)) does not vanish, though we are still able to state a useful result for that case. Some discussion of motivation is presented, in particular as regards to recent gauge-fixing proposals which arise in work that attempts to relate the Gribov ambiguity to confinement.
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