Highly twisted diagrams
Fuente:
arXiv
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| Main Authors: | , , |
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| Format: | Preprint |
| Published: |
2022
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| _version_ | 1866915190149218304 |
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| author | Lazarovich, Nir Moriah, Yoav Pinsky, Tali |
| author_facet | Lazarovich, Nir Moriah, Yoav Pinsky, Tali |
| contents | We prove that the knots and links that admit a 3-highly twisted irreducible diagram with more than two twist regions are hyperbolic. This should be compared with a result of Futer-Purcell for 6-highly twisted diagrams. While their proof uses geometric methods our proof is achieved by showing that the complements of such knots or links are unannular and atoroidal. This is done by using a new approach involving an Euler characteristic argument. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2205_00703 |
| institution | arXiv |
| publishDate | 2022 |
| record_format | arxiv |
| spellingShingle | Highly twisted diagrams Lazarovich, Nir Moriah, Yoav Pinsky, Tali Geometric Topology 57K10, 57K32 We prove that the knots and links that admit a 3-highly twisted irreducible diagram with more than two twist regions are hyperbolic. This should be compared with a result of Futer-Purcell for 6-highly twisted diagrams. While their proof uses geometric methods our proof is achieved by showing that the complements of such knots or links are unannular and atoroidal. This is done by using a new approach involving an Euler characteristic argument. |
| title | Highly twisted diagrams |
| topic | Geometric Topology 57K10, 57K32 |
| url | https://arxiv.org/abs/2205.00703 |