  We show how to cast an interacting system of M--branes into manifestly
gauge-invariant form using an arrangement of higher-dimensional Dirac surfaces.
Classical M--theory has a cohomologically nontrivial and noncommutative set of
gauge symmetries when written using a ``doubled'' formalism containing 3-form
and 6-form gauge fields. We show how the arrangement of Dirac surfaces allows
an integral subgroup of these symmetries to be preserved at the quantum level.
The proper context for discussing these large gauge transformations is relative
cohomology, in which the 3-form transformation parameters become exact when
restricted to the five-brane worldvolume. This structure yields the correct
lattice of M-theory brane charges.
