The vortex-finding property of maximal center (and other) gauges

We argue that the "vortex-finding" property of maximal center gauge, i.e. t he ability of this gauge to locate center vortices inserted by hand on any given lattice, is the key to its success in extracting the vortex content o f thermalized lattice configurations. We explain how this property comes ab out, and why it is expected not only in maximal center gauge, but also in a n infinite class of gauge conditions based on adjoint-representation link v ariables. In principle, the vortex-finding property can be foiled by Gribov copies. This fact is relevant to a gauge-fixing procedure devised by Kovac s and Tomboulis, where we show that the loss of center dominance, found in their procedure, is explained by a corresponding loss of the vortex-finding property. The association of center dominance with the vortex-finding prop erty is demonstrated numerically in a number of other gauges.