Trisected Rainbows and Braids
Fuente:
arXiv
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| Autori principali: | , , , |
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| Natura: | Preprint |
| Pubblicazione: |
2025
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| Soggetti: | |
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| _version_ | 1866916990867734528 |
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| author | Aranda, Román Carter, Scott Courtney, Julia Pongtanapaisan, Puttipong |
| author_facet | Aranda, Román Carter, Scott Courtney, Julia Pongtanapaisan, Puttipong |
| contents | New explicit procedures for passing among triplane diagrams, braid movies, and braid charts for knotted surfaces in $\mathbb{R}^4$ are presented. To this end, rainbow diagrams, which lie between braid charts and triplanes, are introduced. Inequalities relating the braid index and the bridge index of 2-knots are obtained via these procedures. Another consequence is a 4-dimensional version of the classical result that ``the minimal number of Seifert circles equals the braid index of a link'' due to Yamada. The procedures are exemplified for the spun trefoil, the 2-twist spun trefoil, and other related examples.
Of independent interest, an appendix is included that describes a procedure for drawing a triplane diagram for a satellite surface with a 2-sphere companion. Thus, larger families of surfaces for which we know specific triplane diagrams are obtained. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2510_04248 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Trisected Rainbows and Braids Aranda, Román Carter, Scott Courtney, Julia Pongtanapaisan, Puttipong Geometric Topology 57Q45 New explicit procedures for passing among triplane diagrams, braid movies, and braid charts for knotted surfaces in $\mathbb{R}^4$ are presented. To this end, rainbow diagrams, which lie between braid charts and triplanes, are introduced. Inequalities relating the braid index and the bridge index of 2-knots are obtained via these procedures. Another consequence is a 4-dimensional version of the classical result that ``the minimal number of Seifert circles equals the braid index of a link'' due to Yamada. The procedures are exemplified for the spun trefoil, the 2-twist spun trefoil, and other related examples. Of independent interest, an appendix is included that describes a procedure for drawing a triplane diagram for a satellite surface with a 2-sphere companion. Thus, larger families of surfaces for which we know specific triplane diagrams are obtained. |
| title | Trisected Rainbows and Braids |
| topic | Geometric Topology 57Q45 |
| url | https://arxiv.org/abs/2510.04248 |