Danceability, A New Definition of Bridge Index
Fuente:
arXiv
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| Autori principali: | , , , |
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| Natura: | Preprint |
| Pubblicazione: |
2024
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| Soggetti: | |
| Accesso online: | |
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| _version_ | 1866910755512647680 |
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| author | Addison, Sol Scherich, Nancy Snodgrass, Lila Sullivan, Everett |
| author_facet | Addison, Sol Scherich, Nancy Snodgrass, Lila Sullivan, Everett |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2412_15367 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Danceability, A New Definition of Bridge Index Addison, Sol Scherich, Nancy Snodgrass, Lila Sullivan, Everett Geometric Topology 57K10 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. |
| title | Danceability, A New Definition of Bridge Index |
| topic | Geometric Topology 57K10 |
| url | https://arxiv.org/abs/2412.15367 |