Work

Light bulb smoothing for topological surfaces in 4-manifolds

Year: 2025

Type: article

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 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.

Source: Journal of the European Mathematical Society

DOI: 10.4171/jems/1731

Authors: Jae Choon Cha, Byeorhi Kim

Institution: Pohang University of Science and Technology

Language: English

Topic: Geometric and Algebraic Topology

Subfield: Geometry and Topology

Field: Mathematics

Domain: Physical Sciences

Open Access status: diamond

OpenAlex ID: W4414935947

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