A note on the boundary Dehn twist of $K3$ surfaces
Fuente:
arXiv
Enregistré dans:
| Auteur principal: | |
|---|---|
| Format: | Preprint |
| Publié: |
2025
|
| Sujets: | |
| Accès en ligne: | |
| Tags: |
Ajouter un tag
Pas de tags, Soyez le premier à ajouter un tag!
|
| _version_ | 1866909646943420416 |
|---|---|
| author | Lin, Yujie |
| author_facet | Lin, Yujie |
| contents | By the work of Baraglia-Konno and Kronheimer-Mrowka, the boundary Dehn twist on punctured $K3$ surfaces is nontrivial in the smooth mapping class group relative to boundary. In this short note, we prove that it becomes trivial after abelianization. The proof is based on an obstruction for $\mathrm{Spin}^\mathbb{C}$ families due to Baraglia-Konno and the global Torelli theorem of $K3$ surfaces. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2506_10444 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | A note on the boundary Dehn twist of $K3$ surfaces Lin, Yujie Geometric Topology By the work of Baraglia-Konno and Kronheimer-Mrowka, the boundary Dehn twist on punctured $K3$ surfaces is nontrivial in the smooth mapping class group relative to boundary. In this short note, we prove that it becomes trivial after abelianization. The proof is based on an obstruction for $\mathrm{Spin}^\mathbb{C}$ families due to Baraglia-Konno and the global Torelli theorem of $K3$ surfaces. |
| title | A note on the boundary Dehn twist of $K3$ surfaces |
| topic | Geometric Topology |
| url | https://arxiv.org/abs/2506.10444 |