On unique decomposition of knotted handlebodies
Fuente:
arXiv
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| Autori principali: | , , |
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| Natura: | Preprint |
| Pubblicazione: |
2025
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| _version_ | 1866917908548943872 |
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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 |