Knot complements decomposing into prisms
Fuente:
arXiv
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| Auteurs principaux: | , , |
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| Format: | Preprint |
| Publié: |
2025
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| _version_ | 1866915891973718016 |
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| author | DeBlois, Jason Gharagozlou, Arshia Hoffman, Neil R |
| author_facet | DeBlois, Jason Gharagozlou, Arshia Hoffman, Neil R |
| contents | We describe four hyperbolic knot complements in $\mathbb{S}^3$, each of which covers a prism orbifold: the quotient of $\mathbb{H}^3$ by the action of a discrete group generated by reflections in the faces of a polyhedron that has the combinatorial type of a triangular prism. The prism orbifolds are rigid-cusped and contain compact, totally geodesic hyperbolic triangle sub-orbifolds; as a result, the knot complements covering them have hidden symmetries and contain closed, embedded, totally geodesic surfaces. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2507_01263 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Knot complements decomposing into prisms DeBlois, Jason Gharagozlou, Arshia Hoffman, Neil R Geometric Topology 57K32, 57K10 We describe four hyperbolic knot complements in $\mathbb{S}^3$, each of which covers a prism orbifold: the quotient of $\mathbb{H}^3$ by the action of a discrete group generated by reflections in the faces of a polyhedron that has the combinatorial type of a triangular prism. The prism orbifolds are rigid-cusped and contain compact, totally geodesic hyperbolic triangle sub-orbifolds; as a result, the knot complements covering them have hidden symmetries and contain closed, embedded, totally geodesic surfaces. |
| title | Knot complements decomposing into prisms |
| topic | Geometric Topology 57K32, 57K10 |
| url | https://arxiv.org/abs/2507.01263 |