  We find that Polyakov lines, computed in abelian-projected SU(2) lattice
gauge theory in the confined phase, have finite expectation values for lines
corresponding to two units of the abelian electric charge. This means that the
abelian-projected lattice has at most Z(2), rather than U(1), global symmetry.
We also find a severe breakdown of the monopole dominance approximation, as
well as positivity, in this charge-2 case. These results imply that the
abelian-projected lattice is not adequately represented by a monopole Coulomb
gas; the data is, however, consistent with a center vortex structure. Further
evidence is provided, in lattice Monte Carlo simulations, for collimation of
confining color-magnetic flux into vortices.
