  We investigate SU(2) lattice gauge theory in four dimensions in the maximally
abelian projection. Studying the effects on different lattice sizes we show
that the deconfinement transition of the fields and the percolation transition
of the monopole currents in the three space dimensions are precisely related.
To arrive properly at this result the uses of a mathematically sound
characterization of the occurring networks of monopole currents and of an
appropriate method of gauge fixing turn out to be crucial. In addition we
investigate detailed features of the monopole structure in time direction.
