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