| Summary: | For a hyperbolic link K in the thickened torus, we show there is a decomposition of the complement of a link L, obtained from augmenting K, 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 L is hyperbolic. © 2022 World Scientific Publishing Company.
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