A simple proof of the Crowell-Murasugi theorem
Fuente:
arXiv
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| Autor principal: | |
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| Formato: | Preprint |
| Publicado: |
2022
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| Materias: | |
| Acceso en línea: | |
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| _version_ | 1866914925109051392 |
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| author | Kindred, Thomas |
| author_facet | Kindred, Thomas |
| contents | We give an elementary, self-contained proof of the theorem, proven independently in 1958-9 by Crowell and Murasugi, that the genus of an alternating knot equals half the breadth of its Alexander polynomial, and that applying Seifert's algorithm to any alternating knot diagram gives a surface of minimal genus. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2209_09850 |
| institution | arXiv |
| publishDate | 2022 |
| record_format | arxiv |
| spellingShingle | A simple proof of the Crowell-Murasugi theorem Kindred, Thomas Geometric Topology We give an elementary, self-contained proof of the theorem, proven independently in 1958-9 by Crowell and Murasugi, that the genus of an alternating knot equals half the breadth of its Alexander polynomial, and that applying Seifert's algorithm to any alternating knot diagram gives a surface of minimal genus. |
| title | A simple proof of the Crowell-Murasugi theorem |
| topic | Geometric Topology |
| url | https://arxiv.org/abs/2209.09850 |