Article ID | Journal | Published Year | Pages | File Type |
---|---|---|---|---|
5777954 | Topology and its Applications | 2017 | 9 Pages |
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 types 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
Related Topics
Physical Sciences and Engineering
Mathematics
Geometry and Topology
Authors
Noboru Ito, Yusuke Takimura,