Links in the spherical 3-manifold obtained from the quaternion group and their lifts
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arXiv
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| Format: | Preprint |
| Veröffentlicht: |
2024
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| _version_ | 1866912621356122112 |
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| author | Yoshida, Ken'ichi |
| author_facet | Yoshida, Ken'ichi |
| contents | We show that there are infinitely many triples of non-isotopic hyperbolic links in the lens space $L(4,1)$ such that the three lifts of each triple in $S^{3}$ are isotopic. They are obtained as the lifts of links in $S^{3} / Q_{8}$ by double covers, where $Q_{8}$ is the quaternion group. To construct specific examples, we introduce a diagram of a link in $S^{3} / Q_{8}$ obtained by projecting to a square. The diagrams of isotopic links are connected by Reidemeister-type moves. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2409_19303 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Links in the spherical 3-manifold obtained from the quaternion group and their lifts Yoshida, Ken'ichi Geometric Topology 57K10 (Primary) 57K32, 57M10 (Secondary) We show that there are infinitely many triples of non-isotopic hyperbolic links in the lens space $L(4,1)$ such that the three lifts of each triple in $S^{3}$ are isotopic. They are obtained as the lifts of links in $S^{3} / Q_{8}$ by double covers, where $Q_{8}$ is the quaternion group. To construct specific examples, we introduce a diagram of a link in $S^{3} / Q_{8}$ obtained by projecting to a square. The diagrams of isotopic links are connected by Reidemeister-type moves. |
| title | Links in the spherical 3-manifold obtained from the quaternion group and their lifts |
| topic | Geometric Topology 57K10 (Primary) 57K32, 57M10 (Secondary) |
| url | https://arxiv.org/abs/2409.19303 |