English

3-braid knots with maximal 4-genus

Geometric Topology 2024-03-29 v2

Abstract

We classify 3-braid knots whose topological 4-genus coincides with their Seifert genus, using McCoy's twisting method and the Xu normal form. In addition, we give upper bounds for the topological 4-genus of positive and strongly quasipositive 3-braid knots.

Keywords

Cite

@article{arxiv.2303.11918,
  title  = {3-braid knots with maximal 4-genus},
  author = {Sebastian Baader and Lukas Lewark and Filip Misev and Paula Truöl},
  journal= {arXiv preprint arXiv:2303.11918},
  year   = {2024}
}

Comments

24 pages, 7 figures, comments welcome. v2: minor changes, new infinite family of examples in Remark 4.7. Corresponds to published version

R2 v1 2026-06-28T09:26:31.926Z