A spectrum connecting the braid index and the bridge index
Geometric Topology
2024-11-18 v1
Abstract
We study the booklink, a braid-like embedding with local maxima and minima, and the bridge-braid spectrum of a link, which captures the smallest number of braid-strands in a booklink with a prescribed number of critical points. This spectrum spans the gap between the classical bridge and braid indices. We apply a foliation theory argument to provide a formula for the spectra of both split and composite links. We then generate a table for the spectra of all prime knots up to 9 crossings.
Keywords
Cite
@article{arxiv.2411.09845,
title = {A spectrum connecting the braid index and the bridge index},
author = {Margaret Doig and Chase Gehringer},
journal= {arXiv preprint arXiv:2411.09845},
year = {2024}
}
Comments
22 pages, 13 figures, 1 table