  Flag manifolds are shown to describe the relations between configurations of
distinguished points (topologically equivalent to punctures) embedded in a
general spacetime manifold. Grassmannians are flag manifolds with just two
subsets of points selected out from a set of N points. The geometry of
Grassmannians is determined by a group acting by linear fractional
transformations, and the associated Lie algebra induces transitions between
subspaces. Curvature tensors are derived for a general flag manifold, showing
that interactions between a subset of k points and the remaining N-k points in
the configuration is determined by the coordinates in the flag manifold.
