Generalised T-links Represent All Links in the 3-Sphere

Abstract

We introduce generalised T-links, a restricted extension of the widely studied families of T-links and twisted torus links, and prove that this family is universal: every link in the \(3\)-sphere can be represented as a generalised T-link. This gives a compact braid-theoretic form of Ghrist's universality theorem for certain Lorenz-like templates. More precisely, we replace the template-theoretic representatives coming from universal Lorenz-like templates with explicit braid closures depending on finitely many integer parameters. Although closely related braid families have appeared previously in the literature, the universality of this restricted class is the main point of the present paper. Thus, all links in the \(3\)-sphere are placed inside a natural structured class closely related to T-links, Lorenz links, and twisted torus links.

17 pages. 4 figures. Revised version; the material has been reorganized and separated from a longer previous version. This version focuses on generalised T-links