Links in the spherical 3-manifold obtained from the quaternion group and their lifts
| Autor: | Yoshida, Ken'ichi |
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| Rok vydání: | 2024 |
| Předmět: | |
| Druh dokumentu: | Working Paper |
| Popis: | 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. Comment: 15 pages, 16 figures |
| Databáze: | arXiv |
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