Detecting monopoles on the lattice

We address the issue why the number and the location of magnetic monopoles detected on lattice configurations are gauge dependent, in contrast with the physical expectation that monopoles have a gauge-invariant status. By use of the non-Abelian Bianchi identities we show that monopoles are gauge-invariant, but the efficiency of the technique usually adopted to detect them depends on the choice of the gauge in a well understood way. In particular we have studied a class of gauges which interpolate between the Maximal Abelian gauge, where all monopoles are observed, and the Landau gauge, where all monopoles escape detection.