Bridge position of 3-manifolds embedded in the 5-sphere
Fuente:
arXiv
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| Autori principali: | , , , , |
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| Natura: | Preprint |
| Pubblicazione: |
2026
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| _version_ | 1866917406113267712 |
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| author | Aranda, Román Blackwell, Sarah Kim, Geunyoung Naylor, Patrick Pongtanapaisan, Puttipong |
| author_facet | Aranda, Román Blackwell, Sarah Kim, Geunyoung Naylor, Patrick Pongtanapaisan, Puttipong |
| contents | We introduce and study bridge decompositions for 3-manifolds embedded in the 5-sphere. These generalize both the classical notion of bridge position for knots in the 3-sphere and the bridge trisections of surfaces in the 4-sphere due to Meier and Zupan. Our main technical tool is the multisections of 5-manifolds introduced by Aribi, Courte, Golla, and Moussard. We prove that every embedded 3-manifold admits such a decomposition; in particular, any such embedding is encoded by four trivial tangle diagrams. We also present a range of explicit examples, including $S^2$-spun knots and ribbon 3-knots. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2604_12182 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Bridge position of 3-manifolds embedded in the 5-sphere Aranda, Román Blackwell, Sarah Kim, Geunyoung Naylor, Patrick Pongtanapaisan, Puttipong Geometric Topology 57K45, 57K50 We introduce and study bridge decompositions for 3-manifolds embedded in the 5-sphere. These generalize both the classical notion of bridge position for knots in the 3-sphere and the bridge trisections of surfaces in the 4-sphere due to Meier and Zupan. Our main technical tool is the multisections of 5-manifolds introduced by Aribi, Courte, Golla, and Moussard. We prove that every embedded 3-manifold admits such a decomposition; in particular, any such embedding is encoded by four trivial tangle diagrams. We also present a range of explicit examples, including $S^2$-spun knots and ribbon 3-knots. |
| title | Bridge position of 3-manifolds embedded in the 5-sphere |
| topic | Geometric Topology 57K45, 57K50 |
| url | https://arxiv.org/abs/2604.12182 |