A hierarchy of defects in biaxial nematics

We study the topological properties of the manifolds which describe uniaxial and biaxial nematics in order to compare and classify all types of bulk and surface defects that can arise in a nematic liquid crystal. We explain how topological charges can be assigned both to isotropic defects in uniaxial nematics and to uniaxial defects in biaxial nematics; we further see how it is possible to distinguish between isolated surface defects and surface defects which extend in the bulk, and between surface defects which can relax in the bulk and defects forced to stay on the surface

The topological microstructure of defects in nematic liquid crystals

We study the core of line and point defects in nematic liquid crystals. The topological theory of defects allows us to prove that a uniaxial nematic has two ways to avoid a topologically stable defect: either it melts, by becoming isotropic on the putative defect, or a complex biaxial structure arises, that we describe in the paper