Fully Augmented Links in the Thickened Torus

Abstract

In this paper we study the geometry of fully augmented link complements in the thickened torus and describe their geometric properties, generalizing the study of fully augmented links in $S^3$. We classify which fully augmented links in the thickened torus are hyperbolic, show that their complements in the thickened torus decompose into ideal right-angled torihedra, and that the edges of this decomposition are canonical. We also study volume density of fully augmented links in $S^3$, defined to be the ratio of its volume and the number of augmentations. We prove the Volume Density Conjecture for fully augmented links which states that the volume density of a sequence of fully augmented links in $S^3$ which diagrammatically converge to a biperiodic link, converges to the volume density of that biperiodic link.

References in corpus (7)

• Geometrically and diagrammatically maximal knots
• Geometry of biperiodic alternating links
• Volume bounds for generalized twisted torus links
• Volume estimates for equiangular hyperbolic Coxeter polyhedra
• Hyperbolicity of Augmented Links in the Thickened Torus
• Determinant density and biperiodic alternating links
• Generalized Augmented Cellular Alternating Links in Thickened Surfaces are Hyperbolic

Cited by in corpus (1)

• Hyperbolicity of Augmented Links in the Thickened Torus