English

Thirty-two equivalence relations on knot projections

Geometric Topology 2020-12-07 v1

Abstract

We consider 32 homotopy classifications of knot projections (images of generic immersions from a circle into a 2-sphere). These 32 equivalence relations are obtained based on which moves are forbidden among the five type of Reidemeister moves. We show that 32 cases contain 20 non-trivial cases that are mutually different. To complete the proof, we obtain new tools, i.e., new invariants.

Keywords

Cite

@article{arxiv.2012.02612,
  title  = {Thirty-two equivalence relations on knot projections},
  author = {Noboru Ito and Yusuke Takimura},
  journal= {arXiv preprint arXiv:2012.02612},
  year   = {2020}
}

Comments

11 pages, 13 figures

R2 v1 2026-06-23T20:44:02.249Z