English

Null-homologous unknottings

Geometric Topology 2021-07-20 v2

Abstract

Every knot can be unknotted with two generalized twists; this was first proved by Ohyama. Here we prove that any knot of genus g can be unknotted with 2g null-homologous twists and that there exist genus g knots that cannot be unknotted with fewer than 2g null-homologous twists.

Keywords

Cite

@article{arxiv.1902.05405,
  title  = {Null-homologous unknottings},
  author = {Charles Livingston},
  journal= {arXiv preprint arXiv:1902.05405},
  year   = {2021}
}

Comments

Version 2 includes added references

R2 v1 2026-06-23T07:41:03.938Z