A geometric classification of rod complements in the 3-torus
arXiv:2307.06317 · doi:10.1090/proc/16949
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.
15 pages, 1 figure. Two typos corrected, acknowledgements updated. To appear in Proc AMS