The Toulouse–Kleman homotopic classification of topological defects in ordered systems illustrated by experiments
Classification homotopique Toulouse-Kleman de défauts topologiques dans les systèmes ordonnés, illustrée par des expériences
Résumé
We report here on recent experiments with linear topological defects, disclinations in nematics and dislocations in cholesterics, with the aim to illustrate the classification of defects in ordered media based on the homotopy theory conceived by Gérard Toulouse and Maurice Kléman. We focus on objects with double topological character : knotted and linked dislocations in cholesterics. Beside the "\textit{double et tripple anneau}" Hopf links, considered by Toulouse et al., we report on experiments with their generalised version: necklaces made of minimal dislocation loops tethered on cargo dislocations.
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