Thomas Machon, Gareth P. Alexander
Knotted line defects in continuous fields entrain a complex arrangement of the material surrounding them. We characterise knotted nematics through an application of classical knot theory founded upon the Pontryagin-Thom construction for nematic textures. In particular, we show that, despite their non-orientability, nematics detect signed linking numbers and support a countably infinite number of topologically distinct textures through an interplay between topological charge and homology of Seifert surfaces for a given knot. For knots with Milnor fibrations, we give explicit, closed-form constructions for representatives of each topological class.
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http://arxiv.org/abs/1307.6819
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