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.
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