Non-split, alternating links bound unique Seifert surfaces in the 4-ball
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arXiv
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| Main Authors: | , , |
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| Format: | Preprint |
| Published: |
2024
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| _version_ | 1866911372910002176 |
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| author | Kim, Seungwon Miller, Maggie Yoo, Jaehoon |
| author_facet | Kim, Seungwon Miller, Maggie Yoo, Jaehoon |
| contents | We show that any two same-genus, oriented, boundary parallel surfaces bounded by a non-split, alternating link into the 4-ball are smoothly isotopic fixing boundary. In other words, any same-genus Seifert surfaces for a non-split, alternating link become smoothly isotopic fixing boundary once their interiors are pushed into the 4-ball. We conclude that a smooth surface in $S^4$ obtained by gluing two Seifert surfaces for a non-split alternating link is always smoothly unknotted. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2406_11718 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Non-split, alternating links bound unique Seifert surfaces in the 4-ball Kim, Seungwon Miller, Maggie Yoo, Jaehoon Geometric Topology 57K10, 57K45 We show that any two same-genus, oriented, boundary parallel surfaces bounded by a non-split, alternating link into the 4-ball are smoothly isotopic fixing boundary. In other words, any same-genus Seifert surfaces for a non-split, alternating link become smoothly isotopic fixing boundary once their interiors are pushed into the 4-ball. We conclude that a smooth surface in $S^4$ obtained by gluing two Seifert surfaces for a non-split alternating link is always smoothly unknotted. |
| title | Non-split, alternating links bound unique Seifert surfaces in the 4-ball |
| topic | Geometric Topology 57K10, 57K45 |
| url | https://arxiv.org/abs/2406.11718 |