Volume bounds for hyperbolic rod complements in the 3-torus

The study of rod complements is motivated by rod packing structures in crystallography. Each rod packing can be viewed as a geodesic link, or called rods, in the 3-torus. Earlier works have completely classified the geometry of all rod complements. In this talk, we will focus on the volume estimates of hyperbolic rod complements. 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.