A remark on the counterexample to the unknotting number conjecture

Chao Wang; Yimu Zhang

A remark on the counterexample to the unknotting number conjecture

Geometric Topology 2025-07-22 v1

Authors: Chao Wang , Yimu Zhang

Abstract

By using Snappy, M. Brittenham and S. Hermiller discovered a very surprising example that $u(7_1\#\overline{7_1})\leq 5<6=u(7_1)+u(\overline{7_1})$ , where $7_1$ is the $(2,7)$ -torus knot and $\overline{7_1}$ is its mirror image. Based on their work, we give a direct verification of this fact.

Keywords

unknotting number torus knot connected sum counterexample Snappy

Cite

@article{arxiv.2507.14265,
  title  = {A remark on the counterexample to the unknotting number conjecture},
  author = {Chao Wang and Yimu Zhang},
  journal= {arXiv preprint arXiv:2507.14265},
  year   = {2025}
}

Comments

2 pages, 2 figures

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