On symmetry and exterior problems of knotted handlebodies
Fuente:
arXiv
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| Autores principales: | , , |
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| Formato: | Preprint |
| Publicado: |
2025
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| Materias: | |
| Acceso en línea: | |
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| _version_ | 1866908398624178176 |
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| author | Koda, Yuya Ozawa, Makoto Wang, Yi-Sheng |
| author_facet | Koda, Yuya Ozawa, Makoto Wang, Yi-Sheng |
| contents | The paper concerns two classical problems in knot theory pertaining to knot symmetry and knot exteriors. In the context of a knotted handlebody $V$ in a $3$-sphere $S^3$, the symmetry problem seeks to classify the mapping class group of the pair $(S^3,V)$, whereas the exterior problem examines to what extent the exterior $E(V)$ determines or fails to determine the isotopy type of $V$. The paper determines the symmetries of knotted genus two handlebodies arising from hyperbolic knots with non-integral toroidal Dehn surgeries, and solve the knot exterior problem for them. A new interpretation and generalization of a Lee-Lee family of knotted handlebodies is provided. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2506_06713 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | On symmetry and exterior problems of knotted handlebodies Koda, Yuya Ozawa, Makoto Wang, Yi-Sheng Geometric Topology Primary 57K30, Secondary 57M12, 57K10, 57K12 The paper concerns two classical problems in knot theory pertaining to knot symmetry and knot exteriors. In the context of a knotted handlebody $V$ in a $3$-sphere $S^3$, the symmetry problem seeks to classify the mapping class group of the pair $(S^3,V)$, whereas the exterior problem examines to what extent the exterior $E(V)$ determines or fails to determine the isotopy type of $V$. The paper determines the symmetries of knotted genus two handlebodies arising from hyperbolic knots with non-integral toroidal Dehn surgeries, and solve the knot exterior problem for them. A new interpretation and generalization of a Lee-Lee family of knotted handlebodies is provided. |
| title | On symmetry and exterior problems of knotted handlebodies |
| topic | Geometric Topology Primary 57K30, Secondary 57M12, 57K10, 57K12 |
| url | https://arxiv.org/abs/2506.06713 |