$n$-bridge braids and the braid index
Geometric Topology
2023-09-12 v3
Abstract
In this work, we find a closed form formula for the braid index of an -bridge braid, a class of positive braid knots which simultaneously generalizes torus knots, 1-bridge braids, and twisted torus knots. Our proof is elementary, effective, and self-contained, and partially recovers work of Birman--Kofman. Along the way, we show that the disparate definitions of twisted torus knots in the literature agree.
Keywords
Cite
@article{arxiv.2208.13655,
title = {$n$-bridge braids and the braid index},
author = {Dane Gollero and Siddhi Krishna and Marissa Loving and Viridiana Neri and Izah Tahir and Len White},
journal= {arXiv preprint arXiv:2208.13655},
year = {2023}
}
Comments
Accepted to "Journal of Knot Theory and its Ramifications"