On the Cosmetic Crossing Conjecture for Special Alternating Links
Fuente:
arXiv
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| Autor principal: | |
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| Formato: | Preprint |
| Publicado: |
2023
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| _version_ | 1866917868065521664 |
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| author | Boninger, Joe |
| author_facet | Boninger, Joe |
| contents | We prove that a family of links, which includes all special alternating knots, does not admit non-nugatory crossing changes which preserve the isotopy type of the link. Our proof incorporates a result of Lidman and Moore on crossing changes to knots with $L$-space branched double-covers, as well as tools from Scharlemann and Thompon's proof of the cosmetic crossing conjecture for the unknot. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2302_12236 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | On the Cosmetic Crossing Conjecture for Special Alternating Links Boninger, Joe Geometric Topology 57K10 We prove that a family of links, which includes all special alternating knots, does not admit non-nugatory crossing changes which preserve the isotopy type of the link. Our proof incorporates a result of Lidman and Moore on crossing changes to knots with $L$-space branched double-covers, as well as tools from Scharlemann and Thompon's proof of the cosmetic crossing conjecture for the unknot. |
| title | On the Cosmetic Crossing Conjecture for Special Alternating Links |
| topic | Geometric Topology 57K10 |
| url | https://arxiv.org/abs/2302.12236 |