these vortices directly in the SU(2) gauge fields or one can go to the centre gauge [@deldebbio98; @ambjorn98], where one makes the gauge links as close to $+1$ or $-1$ as possible, and construct the corresponding fields where the link matrices take values in Z(2) (‘centre projection’) and where the only nontrivial fluctuations are singular Z(2) vortices. Just as a ’t Hooft–Polyakov monopole will appear as a singular Dirac monopole in the Abelian fields that one obtains after Abelian projection, one would expect the presence of a vortex in the SU(2) fields to appear as a singular Z(2) vortex after centre projection. This picture has received increasing attention recently and has, for example, proved successful in reproducing the static quark potential [@kovacs98; @deldebbio98] (‘centre dominance’). Our ability, in this paper, to address the question of how important are such vortices is constrained by the fact that we only work with Abelian projected SU(2) fields. So first we need to clarify how such vortices might be encoded in these Abelian fields and only then can we perform numerical tests to see whether there is any sign of their presence. This is the content of Sec. \[sec\_mon\_vor\_K\].

Finally there is a summary 