English

Divide knots of maximal genus defect

Geometric Topology 2025-12-15 v2

Abstract

We construct divide knots with arbitrary smooth four-genus but topological four-genus equal to one. In particular, for strongly quasipositive fibred knots, the ratio between the topological and the smooth four-genus can be arbitrarily close to zero.

Keywords

Cite

@article{arxiv.2004.04053,
  title  = {Divide knots of maximal genus defect},
  author = {Livio Liechti},
  journal= {arXiv preprint arXiv:2004.04053},
  year   = {2025}
}

Comments

9 pages, 5 figures

R2 v1 2026-06-23T14:44:24.398Z