Light bulb smoothing for topological surfaces in 4-manifolds

Jae Choon Cha; Byeorhi Kim

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arXiv · 2303.12857

Light bulb smoothing for topological surfaces in 4-manifolds

Jae Choon Cha·Byeorhi Kim

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Abstract

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 Kosanovi\'c-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.

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BibTeX RIS

Jae Choon Cha, Byeorhi Kim. 2023-03-22. Light bulb smoothing for topological surfaces in 4-manifolds. https://arxiv.org/abs/2303.12857

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