Danceability, A New Definition of Bridge Index

• Published in 2024
• Added on 2025-01-07

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.

Links

• http://arxiv.org/abs/2412.15367v1
• http://arxiv.org/pdf/2412.15367v1

Other information

BibTeX entry

@article{DanceabilityANewDefinitionofBridgeIndex,
	key = {DanceabilityANewDefinitionofBridgeIndex},
	type = {article},
	title = {Danceability, A New Definition of Bridge Index},
	author = {Sol Addison and Nancy Scherich and Lila Snodgrass and Everett Sullivan},
	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.},
	comment = {},
	date_added = {2025-01-07},
	date_published = {2024-01-07},
	urls = {http://arxiv.org/abs/2412.15367v1,http://arxiv.org/pdf/2412.15367v1},
	collections = {attention-grabbing-titles},
	url = {http://arxiv.org/abs/2412.15367v1 http://arxiv.org/pdf/2412.15367v1},
	year = 2024,
	urldate = {2025-01-07},
	archivePrefix = {arXiv},
	eprint = {2412.15367},
	primaryClass = {math.GT}
}