2007/07/31 by Joan S. Birman, Joan Birman, Ilya Kofman
Mathematics · #Advanced Combinatorial Mathematics #Bounded function #Braid #Generalization #Geometric and Algebraic Topology #Geometry #Homotopy and Cohomology in Algebraic Topology #Lorenz system #Mathematical analysis #Mathematics #Pure mathematics #Torus #Twist #math.DS #math.GT #msc:37E15 #msc:57M25 #msc:57M27 #msc:57M50
paper · pdf · doi:10.1112/jtopol/jtp007
published as Journal of Topology 2 (2009), 227-248 · This version will be published in J. Topology (2009). 31 pages, 6 figures
openalex publication_date 2009/01/01 · arxiv created 2009/04/21 · arxiv updated 2014/02/26 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05
Twisted torus links are given by twisting a subset of strands on a closed braid representative of a torus link. T-links are a natural generalization given by repeated positive twisting. We establish a one-to-one correspondence between positive braid representatives of Lorenz links and T-links, so Lorenz links and T-links coincide. Using this correspondence, we identify over half of the simplest hyperbolic knots as Lorenz knots. We show that both hyperbolic volume and the Mahler measure of Jones polynomials are bounded for infinite collections of hyperbolic Lorenz links. The correspondence provides unexpected symmetries for both Lorenz links and T-links, and establishes many new results for T-links, including new braid index formulas.