Modular links: bunch algorithm and upper volume bounds
Abstract
In the 1970s, Williams developed an algorithm that has been used to construct and study modular links in the Lorenz template.We introduce an improved algorithm, which we call the bunch algorithm, to provide more insights into the geometry of modular links and Lorenz links.Using the machinery developed for the bunch algorithm, we provide the first upper volume bound that is independent of word exponents and quadratic in the braid index of the Lorenz link component for all modular link complements.We find families of modular knot complements with upper volume bounds that are linear in the braid index.A classification of modular link complements based on the relative magnitudes of word exponents is also presented.
Fields of Study & Subjects
Geometric and Algebraic Topology
Mathematical Dynamics and Fractals
Advanced Combinatorial Mathematics
Publication details
- Journal / source
- Algebraic & Geometric Topology
- Publisher
- Mathematical Sciences Publishers
- Volume
- 26
- Issue
- 6
- Pages
- 2123–2156
- Publication date
- 22 June 2026
- Language
- EN