Light bulb smoothing for topological surfaces in 4-manifolds

Fuente: arXiv
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Main Authors: Cha, Jae Choon, Kim, Byeorhi
Format: Preprint
Published: 2023
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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