Homotopy classification of director fields on polyhedral domains with tangent and periodic boundary conditions, with applications to bi-stable post-aligned liquid crystal displays

We obtain complete topological classification of states of nematic liquid crystal in the geometry of periodic array of rectangular posts between two parallel slabs, with tangent or normal boundary conditions. This classification has applications in bi-stable pos-aligned liquid crystal display design and have technological significance. Methods used in classification are those of algebraic topology and go beyond relative homotopy groups.