Smoothing topological isotopy of surfaces in 4-manifolds with a boundary geometric dual

Jae Choon Cha; Byeorhi Kim

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arXiv · 2609.28598

Smoothing topological isotopy of surfaces in 4-manifolds with a boundary geometric dual

Jae Choon Cha·Byeorhi Kim

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Abstract

We prove that topological isotopy implies smooth isotopy for neat surfaces with common nonempty boundary in a smooth orientable 4-manifold, in the presence of a geometric dual in the boundary. Together with our earlier work on surface smoothing, this shows that the natural map from smooth isotopy classes to topological isotopy classes of such surfaces with prescribed boundary is bijective.

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Jae Choon Cha, Byeorhi Kim. 2026-09-23. Smoothing topological isotopy of surfaces in 4-manifolds with a boundary geometric dual. https://arxiv.org/abs/2609.28598

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