A geometric classification of rod complements in the 3-torus
Fuente:
arXiv
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| Natura: | Preprint |
| Pubblicazione: |
2023
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| _version_ | 1866912780761694208 |
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| author | Hui, Connie On Yu |
| author_facet | Hui, Connie On Yu |
| contents | Rod packings are used in crystallography to describe crystal structures with linear or zigzag chains of particles, and each rod packing can be topologically viewed as a collection of disjoint geodesics in the 3-torus. Hui and Purcell developed a method to study the complements of rods in the 3-torus with the use of 3-dimensional geometry and tools from the 3-sphere, and they partially classified the geometry of some families of rod complements in the 3-torus. In this paper, we provide a complete classification of the geometry of all rod complements in the 3-torus using topological arguments. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2307_06317 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | A geometric classification of rod complements in the 3-torus Hui, Connie On Yu Geometric Topology 57K10, 57K12, 57K32, 57K35 (primary) 57M10, 51M10, 57Z15 (secondary) Rod packings are used in crystallography to describe crystal structures with linear or zigzag chains of particles, and each rod packing can be topologically viewed as a collection of disjoint geodesics in the 3-torus. Hui and Purcell developed a method to study the complements of rods in the 3-torus with the use of 3-dimensional geometry and tools from the 3-sphere, and they partially classified the geometry of some families of rod complements in the 3-torus. In this paper, we provide a complete classification of the geometry of all rod complements in the 3-torus using topological arguments. |
| title | A geometric classification of rod complements in the 3-torus |
| topic | Geometric Topology 57K10, 57K12, 57K32, 57K35 (primary) 57M10, 51M10, 57Z15 (secondary) |
| url | https://arxiv.org/abs/2307.06317 |