A 4-dimensional light bulb theorem for disks
Fuente:
arXiv
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| Format: | Preprint |
| Published: |
2021
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| _version_ | 1866910487856283648 |
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| author | Schwartz, Hannah |
| author_facet | Schwartz, Hannah |
| contents | We give a 4-dimensional light bulb theorem for properly embedded disks, generalizing recent work of Gabai and Kosanovic-Teichner in certain contexts, and extending the 4-dimensional light bulb theorem for 2-spheres due to Gabai and Schneiderman-Teichner. In particular, we provide conditions under which homotopic disks properly embedded in a compact 4-manifold X with a common dual in the interior of X are smoothly isotopic rel boundary. We also provide a new geometric interpretation of the Dax invariant, to aid in its computation. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2109_13397 |
| institution | arXiv |
| publishDate | 2021 |
| record_format | arxiv |
| spellingShingle | A 4-dimensional light bulb theorem for disks Schwartz, Hannah Geometric Topology We give a 4-dimensional light bulb theorem for properly embedded disks, generalizing recent work of Gabai and Kosanovic-Teichner in certain contexts, and extending the 4-dimensional light bulb theorem for 2-spheres due to Gabai and Schneiderman-Teichner. In particular, we provide conditions under which homotopic disks properly embedded in a compact 4-manifold X with a common dual in the interior of X are smoothly isotopic rel boundary. We also provide a new geometric interpretation of the Dax invariant, to aid in its computation. |
| title | A 4-dimensional light bulb theorem for disks |
| topic | Geometric Topology |
| url | https://arxiv.org/abs/2109.13397 |