  Gauge fixing in general is incomplete, such that one solves some of the gauge
constraints, quantizes, then imposes any residual gauge symmetries (Gribov
copies) on the wavefunctions. While the Fadeev-Popov determinant keeps track of
the local metric on this gauge fixed surface, the global topology of the
reduced configuration space can be different depending on the treatment of the
residual symmetries, which can in turn affect global properties of the theory
such as the vacuum wavefunction. Pure $SU(N)$ gauge theory in two dimensions
provides a simple yet non-trivial example where the above structure and effects
can be elucidated explicitly, thus displaying physical effects of the treatment
of Gribov copies.
