  We discuss the construction of the physical configuration space for
Yang-Mills quantum mechanics and Yang-Mills theory on a cylinder. We explicitly
eliminate the redundant degrees of freedom by either fixing a gauge or
introducing gauge invariant variables. Both methods are shown to be equivalent
if the Gribov problem is treated properly and the necessary boundary
identifications on the Gribov horizon are performed. In addition, we analyze
the significance of non-generic configurations and clarify the relation between
the Gribov problem and coordinate singularities.
