Work

Volume bounds for hyperbolic rod complements in the 3-torus

Year: 2025

Type: article

Abstract: The study of rod complements is motivated by rod packing structures in crystallography.We view them as complements of links comprised of Euclidean geodesics in the 3-torus.Recently, Hui classified when such rod complements admit hyperbolic structures, but their geometric properties are yet to be well understood.In this paper, we provide upper and lower bounds for the volumes of all hyperbolic rod complements in terms of rod parameters, and show that these bounds may be loose in general.We introduce better and asymptotically sharp volume bounds for a family of rod complements.The bounds depend only on the lengths of the continued fractions formed from the rod parameters.

Source: Pacific Journal of Mathematics

DOI: 10.2140/pjm.2025.339.167

Authors: Norman Do, Connie On Yu Hui, Jessica S. Purcell

Institution: Monash University

Language: English

Topic: Geometric and Algebraic Topology

Subfield: Geometry and Topology

Field: Mathematics

Domain: Physical Sciences

Open Access status: hybrid

Funder: Australian Research Council

Awards: Geodesic arcs and surfaces for hyperbolic knots and 3-manifolds, Partition functions through the lens of topological recursion