Unknotting number 21 knots are slice in K3
Fuente:
arXiv
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| Autori principali: | , |
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| Natura: | Preprint |
| Pubblicazione: |
2022
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| _version_ | 1866912538019495936 |
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| author | Marengon, Marco Mihajlović, Stefan |
| author_facet | Marengon, Marco Mihajlović, Stefan |
| contents | We prove that all knots with unknotting number at most 21 are smoothly slice in the K3 surface. We also prove a more general statement for 4-manifolds that contain a plumbing tree of spheres. Our strategy is based on a flexible method to remove double points of immersed surfaces in 4-manifolds by tubing over neighbourhoods of embedded trees. As a byproduct, we recover a classical result of Norman and Suzuki that every knot is smoothly slice in $S^2 \times S^2$ and in $\mathbb{CP}^2 \# \overline{\mathbb{CP}^2}$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2210_10089 |
| institution | arXiv |
| publishDate | 2022 |
| record_format | arxiv |
| spellingShingle | Unknotting number 21 knots are slice in K3 Marengon, Marco Mihajlović, Stefan Geometric Topology Primary: 57K10. Secondary: 57K40, 57R10, 57R40, 57R42, 57R45 We prove that all knots with unknotting number at most 21 are smoothly slice in the K3 surface. We also prove a more general statement for 4-manifolds that contain a plumbing tree of spheres. Our strategy is based on a flexible method to remove double points of immersed surfaces in 4-manifolds by tubing over neighbourhoods of embedded trees. As a byproduct, we recover a classical result of Norman and Suzuki that every knot is smoothly slice in $S^2 \times S^2$ and in $\mathbb{CP}^2 \# \overline{\mathbb{CP}^2}$. |
| title | Unknotting number 21 knots are slice in K3 |
| topic | Geometric Topology Primary: 57K10. Secondary: 57K40, 57R10, 57R40, 57R42, 57R45 |
| url | https://arxiv.org/abs/2210.10089 |