A geometric classification of rod complements in the 3-torus

Connie On Yu Hui

doi:10.1090/proc/16949

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arXiv · 2307.06317

A geometric classification of rod complements in the 3-torus

Connie On Yu Hui

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Abstract

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.

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Connie On Yu Hui. 2023-07-12. A geometric classification of rod complements in the 3-torus. https://doi.org/10.1090/proc/16949

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