PreprintarXiv licencearXiv
Smoothing topological isotopy of surfaces in 4-manifolds with a boundary geometric dual
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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BibTeX
@misc{cha2026smoothing,
title = {{Smoothing topological isotopy of surfaces in 4-manifolds with a boundary geometric dual}},
author = {Jae Choon Cha and Byeorhi Kim},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2609.28598},
eprint = {2609.28598},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2609.28598},
}
RIS
TY - UNPB
TI - Smoothing topological isotopy of surfaces in 4-manifolds with a boundary geometric dual
AU - Jae Choon Cha
AU - Byeorhi Kim
PY - 2026
DA - 2026/09/23
PB - arXiv
DO - 10.48550/arxiv.2609.28598
UR - https://arxiv.org/abs/2609.28598
AB - 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.
ER -