Homotopy classification of knotted defects in bounded domains
Soft Condensed Matter
2025-10-28 v1 Mathematical Physics
Geometric Topology
math.MP
Abstract
Nozaki et.~al.\ gave a homotopy classification of the knotted defects of ordered media in three-dimensional space by considering continuous maps from complements of spatial graphs to the order parameter space modulo a certain equivalence relation. We extend their result by giving a classification scheme for ordered media in handlebodies, where defects are allowed to reach the boundary. Through monodromies around meridional loops, global defects are described in terms of planar diagrams whose edges are colored by elements of the fundamental group of the order parameter space. We exhibit examples of this classification in octahedral frame fields and biaxial nematic liquid crystals.
Keywords
Cite
@article{arxiv.2411.03918,
title = {Homotopy classification of knotted defects in bounded domains},
author = {Yuta Nozaki and David Palmer and Yuya Koda},
journal= {arXiv preprint arXiv:2411.03918},
year = {2025}
}
Comments
20 pages, 27 figures