Light bulb smoothing for topological surfaces in 4-manifolds
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arXiv
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| Main Authors: | , |
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| Format: | Preprint |
| Published: |
2023
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| _version_ | 1866913979346976768 |
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| author | Cha, Jae Choon Kim, Byeorhi |
| author_facet | Cha, Jae Choon Kim, Byeorhi |
| contents | We present new smoothing techniques for topologically embedded surfaces in smooth 4-manifolds, which give topological isotopy to a smooth surface. As applications, we prove "topological = smooth" results in dimension 4 for certain disks and spheres modulo isotopy. A key step in our approach is to link Quinn's smoothing theory with ideas in Gabai's 4-dimensional light bulb theorem and succeeding developments of Schneiderman-Teichner and Kosanović-Teichner. As another application of our smoothing technique, we obtain a topological version of the Dax invariant which gives topological isotopy obstructions for topological disks in 4-manifolds. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2303_12857 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Light bulb smoothing for topological surfaces in 4-manifolds Cha, Jae Choon Kim, Byeorhi Geometric Topology 57 We present new smoothing techniques for topologically embedded surfaces in smooth 4-manifolds, which give topological isotopy to a smooth surface. As applications, we prove "topological = smooth" results in dimension 4 for certain disks and spheres modulo isotopy. A key step in our approach is to link Quinn's smoothing theory with ideas in Gabai's 4-dimensional light bulb theorem and succeeding developments of Schneiderman-Teichner and Kosanović-Teichner. As another application of our smoothing technique, we obtain a topological version of the Dax invariant which gives topological isotopy obstructions for topological disks in 4-manifolds. |
| title | Light bulb smoothing for topological surfaces in 4-manifolds |
| topic | Geometric Topology 57 |
| url | https://arxiv.org/abs/2303.12857 |