2024/10/06 by Thiago de Paiva, de Paiva, Thiago, Connie On Yu Hui +3
Engineering · Mathematics · #Architecture and Computational Design #math.DS #math.GT
paper · pdf · doi:10.48550/arxiv.2410.04391
openalex publication_date 2024/10/06 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/30
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.