On Geometric triangulations of double twist knots
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arXiv
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| Auteurs principaux: | , , |
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| Format: | Preprint |
| Publié: |
2025
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| _version_ | 1866916688438493184 |
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| author | Ibarra, Dionne Mathews, Daniel V. Purcell, Jessica S. |
| author_facet | Ibarra, Dionne Mathews, Daniel V. Purcell, Jessica S. |
| contents | In this paper we construct two different explicit triangulations of the family of double twist knots $K(p,q)$ using methods of triangulating Dehn fillings, with layered solid tori and their double covers. One construction yields the canonical triangulation, and one yields a triangulation that we conjecture is minimal. We prove that both are geometric, meaning they are built of positively oriented convex hyperbolic tetrahedra. We use the conjecturally minimal triangulation to present eight equations cutting out the A-polynomial of these knots. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2504_09901 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | On Geometric triangulations of double twist knots Ibarra, Dionne Mathews, Daniel V. Purcell, Jessica S. Geometric Topology Primary: 57Q15. Secondary: 57K10, 57K32, 57K14 In this paper we construct two different explicit triangulations of the family of double twist knots $K(p,q)$ using methods of triangulating Dehn fillings, with layered solid tori and their double covers. One construction yields the canonical triangulation, and one yields a triangulation that we conjecture is minimal. We prove that both are geometric, meaning they are built of positively oriented convex hyperbolic tetrahedra. We use the conjecturally minimal triangulation to present eight equations cutting out the A-polynomial of these knots. |
| title | On Geometric triangulations of double twist knots |
| topic | Geometric Topology Primary: 57Q15. Secondary: 57K10, 57K32, 57K14 |
| url | https://arxiv.org/abs/2504.09901 |