  An efficient way of resolving Gauss' law in Yang-Mills theory is presented by
starting from the projected gauge invariant partition function and integrating
out one spatial field variable. In this way one obtains immediately the
description in terms of unconstrained gauge invariant variables which was
previously obtained by explicitly resolving Gauss' law in a modified axial
gauge. In this gauge, which is a variant of 't Hooft's Abelian gauges, magnetic
monopoles occur. It is shown how the Pontryagin index of the gauge field is
related to the magnetic charges. It turns out that the magnetic monopoles are
sufficient to account for the non-trivial topological structure of the theory.
