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Experiments with cholesterics confined between cylindrical mica sheets have shown that the pattern of dislocations in this geometry is more complex than the expected system of concentric dislocation loops.
System of concentric dislocation loops expected theoretically in the cylinder/cylinder wedge geometry.
In experiments, the concentric dislocation loops generated by the compressive strain in the cylinder/cylinder wedge geometry are interconnected by crossings. This observation rised the issue of the existence of knots and links made of cholesteric dislocations.
Generation of the trefoil knot
Nucleation of a dislocation loop wih six crossings
... by coalescence of two unknots folded twice
Reduction of the number of crossings from 6 to3 by means of the Reidemeister moves conserving the topology.
Conclusion: the dislocation loop with six crossings is topologically equivalent to the trefoil knot.
Generation of the Hopf link
Experiment
Simulation
Changes of the conformation of the Hopf link driven by moduclation of the cylinder/cylinder gap thickness.
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