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arXiv · 2602.20441

An algorithm for Seifert surfaces in 3-manifolds via surgery presentations

Geunyoung Kim
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Abstract

The classical Seifert algorithm provides an explicit construction of a Seifert surface for any link in $S^3$. Alegria and Menasco extended this construction to integral homology $3$-spheres using Heegaard splittings. In this paper, we extend the Seifert algorithm to null-homologous links in arbitrary $3$-manifolds via surgery on framed links in $S^3$.

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Geunyoung Kim. 2026-02-24. An algorithm for Seifert surfaces in 3-manifolds via surgery presentations. https://arxiv.org/abs/2602.20441

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