  Smectic liquid crystals are charcterized by layers that have a preferred
uniform spacing and vanishing curvature in their ground state. Dislocations in
the smectics play an important role in phase nucleation, layer reorientation,
and dynamics. Typically modeled as possessing one line singularity, the layer
structure of a dislocation leads to a diverging compression strain as one
approaches the defect center, suggesting a large, elastically determined melted
core. However, it has been observed that for large charge dislocations, the
defect breaks up into two disclinations [C. E. Williams, Philos. Mag. 32, 313
(1975)]. Here we investigate the topology of the composite core. Because the
smectic cannot twist, transformations between different disclination geometries
are highly constrained. We demonstrate the geometric route between them and
show that despite enjoying precisely the topological rules of the
three-dimensional nematic, the additional structure of line disclinations in
three-dimensional smectics localizes transitions to higher-order point
singularities.
