Geometric Aspects of Singular Dislocations
  The theory of singular dislocations is placed within the framework of the theory of continuous dislocations using de Rham currents. For a general $n$-dimensional manifold, an $(n-1)$-current describes a local layering structure and its boundary in the sense of currents represents the structure of the dislocations. Frank's rules for dislocations follow naturally from the nilpotency of the boundary operator. 
Marcelo Epstein and Reuven Segev
math-ph math.MP