The Plain Sphere Number of a Link
Fuente:
arXiv
Enregistré dans:
| Auteurs principaux: | , , |
|---|---|
| Format: | Preprint |
| Publié: |
2025
|
| Sujets: | |
| Accès en ligne: | |
| Tags: |
Ajouter un tag
Pas de tags, Soyez le premier à ajouter un tag!
|
| _version_ | 1866915963416346624 |
|---|---|
| author | Blair, Ryan Kjuchukova, Alexandra Pfaff, Ella |
| author_facet | Blair, Ryan Kjuchukova, Alexandra Pfaff, Ella |
| contents | Let $L$ be a link in $S^3$. We consider the class of meridional presentations for $π_1(S^3\backslash L)$ in which the relations are witnessed by embedded two-spheres which can be represented simultaneously in a fixed diagram of $L$, analogously to decomposition spheres studied by Cromwell, Menasco and others. Wirtinger relations are witnessed by such spheres and the Wirtinger presentation is a special case of the ones we study. We prove that the smallest number of generators of $π_1(S^3\backslash L)$ over all such presentations equals the bridge number of $L$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2504_10517 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | The Plain Sphere Number of a Link Blair, Ryan Kjuchukova, Alexandra Pfaff, Ella Geometric Topology Let $L$ be a link in $S^3$. We consider the class of meridional presentations for $π_1(S^3\backslash L)$ in which the relations are witnessed by embedded two-spheres which can be represented simultaneously in a fixed diagram of $L$, analogously to decomposition spheres studied by Cromwell, Menasco and others. Wirtinger relations are witnessed by such spheres and the Wirtinger presentation is a special case of the ones we study. We prove that the smallest number of generators of $π_1(S^3\backslash L)$ over all such presentations equals the bridge number of $L$. |
| title | The Plain Sphere Number of a Link |
| topic | Geometric Topology |
| url | https://arxiv.org/abs/2504.10517 |