On the geometry of rod packings in the 3-torus
arXiv:2212.04662 · doi:10.1112/blms.12993
Abstract
Rod packings in the 3-torus encode information of some crystal structures in crystallography. They can be viewed as links in the 3-torus, and tools from 3-manifold geometry and topology can be used to study their complements. In this paper, we initiate the use of geometrisation to study such packings. We analyse the geometric structures of the complements of simple rod packings, and find families that are hyperbolic and Seifert fibred.
arXiv comment20 pages, 8 figures. V2: Minor wording changes, more info on the invariant cubic rod packings added to Section 3