Thirty-two equivalence relations on knot projections
arXiv:2012.02612 · doi:10.1016/j.topol.2017.04.021
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.
11 pages, 13 figures