Smoothly slice links in $\mathbb{CP}^2 \# \overline{\mathbb{CP}^2}$
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arXiv
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| Auteurs principaux: | , |
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| Format: | Preprint |
| Publié: |
2024
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| _version_ | 1866913577548382208 |
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| author | Marengon, Marco McDonald, Clayton |
| author_facet | Marengon, Marco McDonald, Clayton |
| contents | We show that there exists a link with 2 components which is not smoothly slice in $\mathbb{CP}^2 \# \overline{\mathbb{CP}^2}$. By contrast, it is well-known that every knot (i.e., link with 1 component) is smoothly slice therein. Our proof uses classical topological and smooth obstructions, as well as constructive arguments to exploit the symmetries of the problem. As a consequence, we show that there are infinitely many integer homology 3-spheres such that if any of them bounds a ribbon integer homology 4-ball, than there exists an exotic $\mathbb{CP}^2 \# \overline{\mathbb{CP}^2}$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2403_00057 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Smoothly slice links in $\mathbb{CP}^2 \# \overline{\mathbb{CP}^2}$ Marengon, Marco McDonald, Clayton Geometric Topology 57K10 (Primary), 57K40 (Secondary) We show that there exists a link with 2 components which is not smoothly slice in $\mathbb{CP}^2 \# \overline{\mathbb{CP}^2}$. By contrast, it is well-known that every knot (i.e., link with 1 component) is smoothly slice therein. Our proof uses classical topological and smooth obstructions, as well as constructive arguments to exploit the symmetries of the problem. As a consequence, we show that there are infinitely many integer homology 3-spheres such that if any of them bounds a ribbon integer homology 4-ball, than there exists an exotic $\mathbb{CP}^2 \# \overline{\mathbb{CP}^2}$. |
| title | Smoothly slice links in $\mathbb{CP}^2 \# \overline{\mathbb{CP}^2}$ |
| topic | Geometric Topology 57K10 (Primary), 57K40 (Secondary) |
| url | https://arxiv.org/abs/2403.00057 |