  We find, in close analogy to abelian dominance in maximal abelian gauge, the
phenomenon of center dominance in maximal center gauge for $SU(2)$ lattice
gauge theory. Maximal center gauge is a gauge-fixing condition that preserves a
residual $Z_2$ gauge symmetry; ``center projection'' is the projection of
$SU(2)$ link variables onto $Z_2$ center elements, and ``center dominance'' is
the fact that the center-projected link elements carry most of the information
about the string tension of the full theory. We present numerical evidence that
the thin $Z_2$ vortices of the projected configurations are associated with
``thick'' $Z_2$ vortices in the unprojected configurations. The evidence also
suggests that the thick $Z_2$ vortices may play a significant role in the
confinement process.
