Hyperbolicity of augmented links in the thickened torus

Abstract

For a hyperbolic link [Formula: see text] in the thickened torus, we show there is a decomposition of the complement of a link [Formula: see text], obtained from augmenting [Formula: see text], into torihedra. We further decompose the torihedra into angled pyramids and finally angled tetrahedra. These fit into an angled structure on a triangulation of the link complement, and thus by [D. Futer and F. Guéritaud, From angled triangulations to hyperbolic structures, in Interactions between Hyperbolic Geometry, Quantum Topology and Number Theory, Contemporary Mathematics, Vol. 541 (American Mathematical Society, Providence, RI, 2011), pp. 159–182.], this shows that [Formula: see text] is hyperbolic.