The topology of knots and links in nematics

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Abstract

We review some our results concerning the topology of knotted and linked defects in nematic liquid crystals. We discuss the global topological classification of nematic textures with defects, showing how knotted and linked defect lines have a finite number of ‘internal states’, counted by the Alexander polynomial of the knot or link. We then give interpretations of these states in terms of umbilic lines, which we also introduce, as well as planar textures. We show how Milnor polynomials can be used to give explicit constructions of these textures. Finally, we discuss some open problems raised by this work.
Original languageEnglish
Pages (from-to)58-67
Number of pages10
JournalLiquid Crystals
Volume28
Issue number3
Early online date2 Dec 2019
DOIs
Publication statusE-pub ahead of print - 2 Dec 2019

Bibliographical note

The acceptance date for this record is provisional and based upon the month of publication for the article.

Keywords

  • defects
  • topology
  • knots

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