  The notion of G-structure is defined and various geometrical and topological
aspects of such structures are discussed. A particular chain of subgroups in
the affine group for Minkowski space is chosen and the canonical geometrical
and topological objects that are asssociated with each reduction of the bundle
of affine frames on a four-dimensional manifold are detailed. Their physical
significance is discussed in the language of topological defects in ordered
media. Particular attention is paid to how one topologically characterizes the
wave phase of the spacetime vacuum manifold.
