A geometric classification of rod complements in the 3-torus
Geometric Topology
2025-12-23 v3
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.
Keywords
Cite
@article{arxiv.2307.06317,
title = {A geometric classification of rod complements in the 3-torus},
author = {Connie On Yu Hui},
journal= {arXiv preprint arXiv:2307.06317},
year = {2025}
}
Comments
15 pages, 1 figure. Two typos corrected, acknowledgements updated. To appear in Proc AMS