title: Knot theory realizations in nematic colloids.
abstract: Nematic braids are reconfigurable knots and links formed by the disclination loops that entangle colloidal particles dispersed in a nematic liquid crystal. We focus on entangled nematic disclinations in thin twisted nematic layers stabilized by 2D arrays of colloidal particles that can be controlled with laser tweezers. We take the experimentally assembled structures and demonstrate the correspondence of the knot invariants, constructed graphs, and surfaces associated with the disclination loop to the physically observable features specific to the geometry at hand. The nematic nature of the medium adds additional topological parameters to the conventional results of knot theory, which couple with the knot topology and introduce order into the phase diagram of possible structures. The crystalline order allows the simplified construction of the Jones polynomial and medial graphs, and the steps in the construction algorithm are mirrored in the physics of liquid crystals.
authors.affiliation: Faculty of Mathematics and Physics, University of Ljubljana, 1000 Ljubljana, Slovenia;
authors.forename: Simon
authors.initials: S
authors.lastname: Čopar
authors.affiliation: Jožef Stefan Institute, 1000 Ljubljana, Slovenia; and Faculty of Natural Sciences and Mathematics, University of Maribor, 2000 Maribor, Slovenia uros.tkalec@ijs.si.
authors.forename: Uroš
authors.initials: U
authors.lastname: Tkalec
authors.affiliation: Faculty of Mathematics and Physics, University of Ljubljana, 1000 Ljubljana, Slovenia; Jožef Stefan Institute, 1000 Ljubljana, Slovenia; and.
authors.forename: Igor
authors.initials: I
authors.lastname: Muševič
authors.affiliation: Faculty of Mathematics and Physics, University of Ljubljana, 1000 Ljubljana, Slovenia; Jožef Stefan Institute, 1000 Ljubljana, Slovenia; and.
authors.forename: Slobodan
authors.initials: S
authors.lastname: Žumer
keywords: knot theory; knotted fields; liquid crystal colloids; topological defects