Homotopy classification of knotted defects in bounded domains
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arXiv
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| Auteurs principaux: | , , |
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| Format: | Preprint |
| Publié: |
2024
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| _version_ | 1866915578101366784 |
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| author | Nozaki, Yuta Palmer, David Koda, Yuya |
| author_facet | Nozaki, Yuta Palmer, David Koda, Yuya |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2411_03918 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Homotopy classification of knotted defects in bounded domains Nozaki, Yuta Palmer, David Koda, Yuya Soft Condensed Matter Mathematical Physics Geometric Topology 57Z05 (Primary) 57K10, 76A15 (Secondary) 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. |
| title | Homotopy classification of knotted defects in bounded domains |
| topic | Soft Condensed Matter Mathematical Physics Geometric Topology 57Z05 (Primary) 57K10, 76A15 (Secondary) |
| url | https://arxiv.org/abs/2411.03918 |