English

A counterexample to the Bernhard-Jablan unknotting conjecture

Geometric Topology 2018-01-03 v2

Abstract

We show that there is a knot satisfying the property that for each minimal crossing number diagram of the knot and each single crossing of the diagram, changing the crossing results in a diagram for a knot whose unknotting number is at least that of the original knot, thus giving a counterexample to the Bernhard-Jablan Conjecture.

Keywords

Cite

@article{arxiv.1705.05985,
  title  = {A counterexample to the Bernhard-Jablan unknotting conjecture},
  author = {Mark Brittenham and Susan Hermiller},
  journal= {arXiv preprint arXiv:1705.05985},
  year   = {2018}
}

Comments

15 pages, 3 figures. Version 2 is a substantial revision and reorganization

R2 v1 2026-06-22T19:49:23.668Z