Modular links: Bunch algorithm and upper volume bounds

Fuente: arXiv
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Auteurs principaux: Hui, Connie On Yu, Migueles, José Andrés Rodríguez
Format: Preprint
Publié: 2023
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author Hui, Connie On Yu
Migueles, José Andrés Rodríguez
author_facet Hui, Connie On Yu
Migueles, José Andrés Rodríguez
contents 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.
format Preprint
id arxiv_https___arxiv_org_abs_2308_12847
institution arXiv
publishDate 2023
record_format arxiv
spellingShingle Modular links: Bunch algorithm and upper volume bounds
Hui, Connie On Yu
Migueles, José Andrés Rodríguez
Geometric Topology
Dynamical Systems
57K10, 57K32 (primary) 37D40, 37E35 (secondary)
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.
title Modular links: Bunch algorithm and upper volume bounds
topic Geometric Topology
Dynamical Systems
57K10, 57K32 (primary) 37D40, 37E35 (secondary)
url https://arxiv.org/abs/2308.12847