  We cast M-brane interactions including intersecting membranes and five-branes
in manifestly gauge invariant form using an arrangement of higher dimensional
Dirac surfaces. We show that the noncommutative gauge symmetry present in the
doubled M-theory formalism involving dual 3-form and 6-form gauge fields is
preserved in a form quantised over the integers. The proper context for
discussing large noncommutative gauge transformations is relative cohomology,
in which the 3-form transformation parameters become exact when restricted to
the five-brane worldvolume. We show how this structure yields the lattice of
M-theory charges and gives rise to the conjectured 7D Hopf-Wess-Zumino term.
