Bridge position of 3-manifolds embedded in the 5-sphere

Fuente: arXiv
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Autori principali: Aranda, Román, Blackwell, Sarah, Kim, Geunyoung, Naylor, Patrick, Pongtanapaisan, Puttipong
Natura: Preprint
Pubblicazione: 2026
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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