Research ArticleNo Access

Hyperbolicity of augmented links in the thickened torus

Alice Kwon

Department of Science, SUNY Maritime, 6 Pennyfield Avenue, Bronx, NY 10465, USA

E-mail Address: akwon@sunymaritime.edu

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and

Ying Hong Tham

Department of Mathematics, Stony Brook University, 100 Nicolls Road, Stony Brook, NY 11794, USA

E-mail Address: thamyinghong@gmail.com

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https://doi.org/10.1142/S0218216522500250Cited by:1 (Source: Crossref)

Abstract

For a hyperbolic link $K$ $K$ in the thickened torus, we show there is a decomposition of the complement of a link $L$ $L$ , obtained from augmenting $K$ $K$ , 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 $L$ $L$ is hyperbolic.

Keywords:

AMSC: 57K10, 57K33

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