The slice-Bennequin inequality for the fractional Dehn twist coefficient
Fuente:
arXiv
Salvato in:
| Autore principale: | |
|---|---|
| Natura: | Preprint |
| Pubblicazione: |
2022
|
| Soggetti: | |
| Accesso online: | |
| Tags: |
Aggiungi Tag
Nessun Tag, puoi essere il primo ad aggiungerne!!
|
| _version_ | 1866915102446321664 |
|---|---|
| author | Feller, Peter |
| author_facet | Feller, Peter |
| contents | We characterize the fractional Dehn twist coefficient (FDTC) on the $n$-stranded braid group as the unique homogeneous quasimorphism to the real numbers of defect at most 1 that equals 1 on the positive full twist and vanishes on the $(n-1)$-stranded braid subgroup. In a different direction, we establish that the slice-Bennequin inequality holds with the FDTC in place of the writhe. In other words, we establish an affine linear lower bound for the smooth slice genus of the closure of a braid in terms of the braid's FDTC. We also discuss connections between these two seemingly unrelated results. In the appendix we provide a unifying framework for the slice-Bennequin inequality and its counterpart for the FDTC. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2204_05288 |
| institution | arXiv |
| publishDate | 2022 |
| record_format | arxiv |
| spellingShingle | The slice-Bennequin inequality for the fractional Dehn twist coefficient Feller, Peter Geometric Topology 57K20, 57K10 We characterize the fractional Dehn twist coefficient (FDTC) on the $n$-stranded braid group as the unique homogeneous quasimorphism to the real numbers of defect at most 1 that equals 1 on the positive full twist and vanishes on the $(n-1)$-stranded braid subgroup. In a different direction, we establish that the slice-Bennequin inequality holds with the FDTC in place of the writhe. In other words, we establish an affine linear lower bound for the smooth slice genus of the closure of a braid in terms of the braid's FDTC. We also discuss connections between these two seemingly unrelated results. In the appendix we provide a unifying framework for the slice-Bennequin inequality and its counterpart for the FDTC. |
| title | The slice-Bennequin inequality for the fractional Dehn twist coefficient |
| topic | Geometric Topology 57K20, 57K10 |
| url | https://arxiv.org/abs/2204.05288 |