Alternating links have at most polynomially many Seifert surfaces of fixed genus
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arXiv
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| Main Authors: | , , |
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| Format: | Preprint |
| Published: |
2018
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| _version_ | 1866914970634027008 |
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| author | Hass, Joel Thompson, Abigail Tsvietkova, Anastasiia |
| author_facet | Hass, Joel Thompson, Abigail Tsvietkova, Anastasiia |
| contents | Let $L$ be a non-split prime alternating link with $n>0$ crossings. We show that for each fixed $g$, the number of genus-$g$ Seifert surfaces for $L$ is bounded by an explicitly given polynomial in $n$. The result also holds for all spanning surfaces of fixed Euler characteristic. Previously known bounds were exponential. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_1809_10996 |
| institution | arXiv |
| publishDate | 2018 |
| record_format | arxiv |
| spellingShingle | Alternating links have at most polynomially many Seifert surfaces of fixed genus Hass, Joel Thompson, Abigail Tsvietkova, Anastasiia Geometric Topology 57M25 Let $L$ be a non-split prime alternating link with $n>0$ crossings. We show that for each fixed $g$, the number of genus-$g$ Seifert surfaces for $L$ is bounded by an explicitly given polynomial in $n$. The result also holds for all spanning surfaces of fixed Euler characteristic. Previously known bounds were exponential. |
| title | Alternating links have at most polynomially many Seifert surfaces of fixed genus |
| topic | Geometric Topology 57M25 |
| url | https://arxiv.org/abs/1809.10996 |