  We consider topological constraints that must be satisfied by formulations of
gravitation as a gauge theory. To facilitate the analysis we review and further
justify the composite bundle formalism of Tresguerres as a consistent
underlying structure capable of incorporating both the local Lorentz and
translational degrees of freedom. Identifying an important global structure
required by the composite construction, we translate this into conditions on
the underlying manifold. We find that in addition to admitting the expected
orientability, causality and spin structures, the underlying manifold must also
admit a string structure. We take this to imply that even before considerations
of quantum consistency, topological considerations of gauge gravity provide a
classical motivation for extended degrees of freedom.
