Danceability, A New Definition of Bridge Index
Geometric Topology
2024-12-23 v1
Abstract
There are three commonly known definitions of the bridge index. These definitions come from combinatorial knot theory, Morse theory, and geometry. In this paper, we prove that the danceability index is a fourth equivalent definition of the bridge index. We extend the danceability invariant to virtual knots in multiple ways and compare these invariants to two different notions of bridge index for virtual knots.
Cite
@article{arxiv.2412.15367,
title = {Danceability, A New Definition of Bridge Index},
author = {Sol Addison and Nancy Scherich and Lila Snodgrass and Everett Sullivan},
journal= {arXiv preprint arXiv:2412.15367},
year = {2024}
}