On unique decomposition of knotted handlebodies

Fuente: arXiv
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Autores principales: Bellettini, Giovanni, Paolini, Maurizio, Wang, Yi-Sheng
Formato: Preprint
Publicado: 2025
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author Bellettini, Giovanni
Paolini, Maurizio
Wang, Yi-Sheng
author_facet Bellettini, Giovanni
Paolini, Maurizio
Wang, Yi-Sheng
contents The paper considers the uniqueness question of factorization of a knotted handlebody in the $3$-sphere along decomposing $2$-spheres. We obtain a uniqueness result for factorization along decomposing $2$-spheres meeting the handlebody at three parallel disks. The result is used to examine handlebody-knot symmetry; particularly, the chirality of $6_{10}$ in the handlebody-knot table, previously unknown, is determined. In addition, an infinite family of hyperbolic handlebody-knots with homeomorphic exteriors is constructed.
format Preprint
id arxiv_https___arxiv_org_abs_2502_00422
institution arXiv
publishDate 2025
record_format arxiv
spellingShingle On unique decomposition of knotted handlebodies
Bellettini, Giovanni
Paolini, Maurizio
Wang, Yi-Sheng
Geometric Topology
primary 57K12, secondary 57K30, 57M15
The paper considers the uniqueness question of factorization of a knotted handlebody in the $3$-sphere along decomposing $2$-spheres. We obtain a uniqueness result for factorization along decomposing $2$-spheres meeting the handlebody at three parallel disks. The result is used to examine handlebody-knot symmetry; particularly, the chirality of $6_{10}$ in the handlebody-knot table, previously unknown, is determined. In addition, an infinite family of hyperbolic handlebody-knots with homeomorphic exteriors is constructed.
title On unique decomposition of knotted handlebodies
topic Geometric Topology
primary 57K12, secondary 57K30, 57M15
url https://arxiv.org/abs/2502.00422