English

$n$-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 nn-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"

R2 v1 2026-06-25T02:03:34.887Z