title: Global defect topology in nematic liquid crystals.
abstract: We give the global homotopy classification of nematic textures for a general domain with weak anchoring boundary conditions and arbitrary defect set in terms of twisted cohomology, and give an explicit computation for the case of knotted and linked defects in [Formula: see text], showing that the distinct homotopy classes have a 1-1 correspondence with the first homology group of the branched double cover, branched over the disclination loops. We show further that the subset of those classes corresponding to elements of order 2 in this group has representatives that are planar and characterize the obstruction for other classes in terms of merons. The planar textures are a feature of the global defect topology that is not reflected in any local characterization. Finally, we describe how the global classification relates to recent experiments on nematic droplets and how elements of order 4 relate to the presence ofτlines in cholesterics.
authors: Department of Physics and Centre for Complexity Science , University of Warwick , Coventry CV4 7AL, UK.
authors: Thomas
authors: T
authors: Machon
authors: Department of Physics and Centre for Complexity Science , University of Warwick , Coventry CV4 7AL, UK.
authors: Gareth P
authors: 0000-0003-2862-108X
authors: GP
authors: Alexander
keywords: knot theory; liquid crystals; topological defects