  We shall give a twisted Dirac structure on the space of irreducible
connections on a SU(n)-bundle over a three-manifold, and give a family of
twisted Dirac structures on the space of irreducible connections on the trivial
SU(n)-bundle over a four-manifold. The twist is described by the Cartan 3-form
on the space of connections. It vanishes over the subspace of flat connections.
So the spaces of flat connections are endowed with ( non-twisted ) Dirac
structures. The Dirac structure on the space of flat connections over the
three-manifold is obtained as the boundary restriction of a corresponding Dirac
structure over the four-manifold. We discuss also the action of the group of
gauge transformations over these Dirac structures.
