Cyclic branched covers of Seifert links and properties related to the $ADE$ link conjecture
Fuente:
arXiv
Guardado en:
| Autores principales: | , , |
|---|---|
| Formato: | Preprint |
| Publicado: |
2024
|
| Materias: | |
| Acceso en línea: | |
| Etiquetas: |
Agregar Etiqueta
Sin Etiquetas, Sea el primero en etiquetar este registro!
|
| _version_ | 1866913244085485568 |
|---|---|
| author | Boyer, Steven Gordon, Cameron McA. Hu, Ying |
| author_facet | Boyer, Steven Gordon, Cameron McA. Hu, Ying |
| contents | In this article we show that all cyclic branched covers of a Seifert link have left-orderable fundamental groups, and therefore admit co-oriented taut foliations and are not $L$-spaces, if and only if it is not an $ADE$ link up to orientation. This leads to a proof of the $ADE$ link conjecture for Seifert links. When $L$ is an $ADE$ link up to orientation, we determine which of its canonical $n$-fold cyclic branched covers $Σ_n(L)$ have non-left-orderable fundamental groups. In addition, we give a topological proof of Ishikawa's classification of strongly quasipositive Seifert links and we determine the Seifert links that are definite, resp. have genus zero, resp. have genus equal to its smooth $4$-ball genus, among others. In the last section, we provide a comprehensive survey of the current knowledge and results concerning the $ADE$ link conjecture. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2402_15914 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Cyclic branched covers of Seifert links and properties related to the $ADE$ link conjecture Boyer, Steven Gordon, Cameron McA. Hu, Ying Geometric Topology 57M12, 57M50, 57M99 In this article we show that all cyclic branched covers of a Seifert link have left-orderable fundamental groups, and therefore admit co-oriented taut foliations and are not $L$-spaces, if and only if it is not an $ADE$ link up to orientation. This leads to a proof of the $ADE$ link conjecture for Seifert links. When $L$ is an $ADE$ link up to orientation, we determine which of its canonical $n$-fold cyclic branched covers $Σ_n(L)$ have non-left-orderable fundamental groups. In addition, we give a topological proof of Ishikawa's classification of strongly quasipositive Seifert links and we determine the Seifert links that are definite, resp. have genus zero, resp. have genus equal to its smooth $4$-ball genus, among others. In the last section, we provide a comprehensive survey of the current knowledge and results concerning the $ADE$ link conjecture. |
| title | Cyclic branched covers of Seifert links and properties related to the $ADE$ link conjecture |
| topic | Geometric Topology 57M12, 57M50, 57M99 |
| url | https://arxiv.org/abs/2402.15914 |