A new twist on Lorenz links
By J. Birman, Ilya Kofman. 2007
66 citations recorded by the source corpus.
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.
Subfields: Discrete Mathematics and Combinatorics, Geometry and Topology, Mathematical Physics
View Paper: https://www.semanticscholar.org/paper/501e3826c9ddbe27154275f443d4ab162af8d38d
How researchers see this paper
The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.
In Discrete Mathematics and Combinatorics
In Geometry and Topology
In Mathematical Physics
Citations in the corpus
- Infinitely many Lagrangian fillings (2020, background): “6 can be chosen to be cable knots, and the hyperbolic knots we will exhibit are also well-beloved [7, 38].”