Structure and classification of torus theta-curves
Fuente:
arXiv
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| Autores principales: | , |
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| Formato: | Preprint |
| Publicado: |
2025
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| _version_ | 1866917370834976768 |
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| author | Calcut, Jack S. Nieman, Samantha E. |
| author_facet | Calcut, Jack S. Nieman, Samantha E. |
| contents | We study theta-curves embedded in a standard torus in the 3-sphere. We show that each nontrivial torus knot together with an essential arc determines a prime theta-curve, yielding explicit infinite families of prime theta-curves. We compute their constituent knots and identify the structure governing these embeddings, which leads to a complete classification of torus theta-curves up to ambient isotopy and homeomorphism of the 3-sphere. In particular, Kinoshita's theta-curve does not lie on a standard torus. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2511_09848 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Structure and classification of torus theta-curves Calcut, Jack S. Nieman, Samantha E. Geometric Topology 57K10 (Primary), 57M15 (Secondary), 05C10 (Secondary) We study theta-curves embedded in a standard torus in the 3-sphere. We show that each nontrivial torus knot together with an essential arc determines a prime theta-curve, yielding explicit infinite families of prime theta-curves. We compute their constituent knots and identify the structure governing these embeddings, which leads to a complete classification of torus theta-curves up to ambient isotopy and homeomorphism of the 3-sphere. In particular, Kinoshita's theta-curve does not lie on a standard torus. |
| title | Structure and classification of torus theta-curves |
| topic | Geometric Topology 57K10 (Primary), 57M15 (Secondary), 05C10 (Secondary) |
| url | https://arxiv.org/abs/2511.09848 |