Non-split, alternating links bound unique Seifert surfaces in the 4-ball
Geometric Topology
2026-01-14 v2
Abstract
We show that any two same-genus, oriented, boundary parallel surfaces bounded by a non-split, alternating link into the 4-ball are smoothly isotopic fixing boundary. In other words, any same-genus Seifert surfaces for a non-split, alternating link become smoothly isotopic fixing boundary once their interiors are pushed into the 4-ball. We conclude that a smooth surface in obtained by gluing two Seifert surfaces for a non-split alternating link is always smoothly unknotted.
Cite
@article{arxiv.2406.11718,
title = {Non-split, alternating links bound unique Seifert surfaces in the 4-ball},
author = {Seungwon Kim and Maggie Miller and Jaehoon Yoo},
journal= {arXiv preprint arXiv:2406.11718},
year = {2026}
}
Comments
9 pages, 3 figures