Triangulations of the 3-sphere with knotted edge
Fuente:
arXiv
Gespeichert in:
| Hauptverfasser: | , , , |
|---|---|
| Format: | Preprint |
| Veröffentlicht: |
2024
|
| Schlagworte: | |
| Online-Zugang: | |
| Tags: |
Tag hinzufügen
Keine Tags, Fügen Sie den ersten Tag hinzu!
|
| _version_ | 1866915039525470208 |
|---|---|
| author | Ibarra, Dionne Mathews, Daniel V. Purcell, Jessica S. Spreer, Jonathan |
| author_facet | Ibarra, Dionne Mathews, Daniel V. Purcell, Jessica S. Spreer, Jonathan |
| contents | We prove that for any knot $K$, there exists a one-vertex triangulation of the $3$-sphere containing an edge forming $K$. The proof is constructive, and based on fully augmented links. We use our method to produce ``complicated'' simplicial triangulations of the $3$-sphere that we show are smallest possible, up to a constant multiplicative factor. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2411_18938 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Triangulations of the 3-sphere with knotted edge Ibarra, Dionne Mathews, Daniel V. Purcell, Jessica S. Spreer, Jonathan Geometric Topology Primary: 57Q15. Secondary: 57K32, 57K31, 57K10, 57Q70 We prove that for any knot $K$, there exists a one-vertex triangulation of the $3$-sphere containing an edge forming $K$. The proof is constructive, and based on fully augmented links. We use our method to produce ``complicated'' simplicial triangulations of the $3$-sphere that we show are smallest possible, up to a constant multiplicative factor. |
| title | Triangulations of the 3-sphere with knotted edge |
| topic | Geometric Topology Primary: 57Q15. Secondary: 57K32, 57K31, 57K10, 57Q70 |
| url | https://arxiv.org/abs/2411.18938 |