  The homotopy theory of topological defects in ordered media fails to
completely characterize systems with broken translational symmetry. We argue
that the problem can be understood in terms of the lack of rotational Goldstone
modes in such systems and provide an alternate approach that correctly accounts
for the interaction between translations and rotations. Dislocations are
associated, as usual, with branch points in a phase field, while disclinations
arise as critical points and singularities in the phase field. We introduce a
three-dimensional model for two-dimensional smectics that clarifies the
topology of disclinations and geometrically captures known results without the
need for compatibility conditions. Our work suggests natural generalizations of
the two-dimensional smectic theory to higher dimensions and to crystals.
