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.
Cite
@article{arxiv.2308.12847,
title = {Modular links: Bunch algorithm and upper volume bounds},
author = {Connie On Yu Hui and José Andrés Rodríguez Migueles},
journal= {arXiv preprint arXiv:2308.12847},
year = {2025}
}
Comments
37 pages, 14 figures. V2: Same mathematical content, main changes made based on reviewer's comments: added an example of using Williams' algorithm and improved the exposition