  We investigate the relationship between colour confinement and topological
structures derived from the gauge invariant Abelian (Cho-Duan-Ge)
decomposition. This Abelian decomposition is made imposing an isometry on a
colour field $n$ which selects the Abelian direction; the principle novelty of
our study is that we have defined this field in terms of the eigenvectors of
the Wilson Loop. This allows us to establish an equivalence between the path
ordered integral of the non-Abelian gauge fields with an integral over an
Abelian restricted gauge field which is tractable both theoretically and
numerically in lattice QCD. By using Stokes' theorem, we can relate the Wilson
Loop in terms of a surface integral over a restricted field strength, and show
that the restricted field strength may be dominated by topological structures,
which occur when one of the parameters parametrising the colour field $n$ winds
itself around a non-analyticity in the colour field. If they exist, these
objects will lead to an area law scaling for the Wilson Loop and provide a
mechanism for quark confinement. We search for these structures in quenched
lattice QCD. We perform the Abelian decomposition, and find that the restricted
field strength is dominated by peaks on the lattice. Wilson Loops containing
these peaks show a stronger area-Law and thus provide the dominant contribution
to the string tension.
