Danceability, A New Definition of Bridge Index
Sol Addison, Nancy Scherich, Lila Snodgrass, Everett Sullivan

TL;DR
This paper introduces the danceability index as a new, equivalent definition of the bridge index in knot theory, extending it to virtual knots and comparing it with existing notions.
Contribution
It establishes danceability as a new bridge index definition and extends it to virtual knots, providing a novel perspective in knot invariants.
Findings
Danceability index is equivalent to the bridge index.
Extended danceability to virtual knots in multiple ways.
Compared new invariants with existing virtual knot bridge indices.
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.
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Taxonomy
TopicsDiversity and Impact of Dance
