Tiling the 4-ball with knotted surfaces
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arXiv
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| Hauptverfasser: | , , |
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| Format: | Preprint |
| Veröffentlicht: |
2025
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| _version_ | 1866912374542303232 |
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| author | Ross, James Schwartz, Hannah Ye, Andrew |
| author_facet | Ross, James Schwartz, Hannah Ye, Andrew |
| contents | We show that for any closed, orientable surface $K$ smoothly embedded in $\mathbb{R}^4$, the unit $4$-ball $B^4 \subset \mathbb{R}^4$ can be tiled using $n \geq 3$ tiles each congruent to a regular neighborhood (with corners) of a surface smoothly isotopic to $K$. This gives a 4-dimensional analog of tilings of the $3$-ball that were constructed in the 90's using congruent knotted tori. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2505_08976 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Tiling the 4-ball with knotted surfaces Ross, James Schwartz, Hannah Ye, Andrew Geometric Topology Metric Geometry We show that for any closed, orientable surface $K$ smoothly embedded in $\mathbb{R}^4$, the unit $4$-ball $B^4 \subset \mathbb{R}^4$ can be tiled using $n \geq 3$ tiles each congruent to a regular neighborhood (with corners) of a surface smoothly isotopic to $K$. This gives a 4-dimensional analog of tilings of the $3$-ball that were constructed in the 90's using congruent knotted tori. |
| title | Tiling the 4-ball with knotted surfaces |
| topic | Geometric Topology Metric Geometry |
| url | https://arxiv.org/abs/2505.08976 |