  We express the Pontryagin index in Polyakov gauge completely in terms of
magnetically charged gauge fixing defects, namely magnetic monopoles, lines,
and domain walls. Open lines and domain walls are topologically equivalent to
monopoles, which are the genuine defects. The emergence of non-genuine
magnetically charged closed domain walls can be avoided by choosing the
temporal gauge field smoothly. The Pontryagin index is then exclusively
determined by the magnetic monopoles.
