Thirty-two equivalence relations on knot projections

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...

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Bibliographic Details
Published in:Topology and its applications 2017-07, Vol.225, p.130-138
Main Authors: Ito, Noboru, Takimura, Yusuke
Format: Article
Language:English
Subjects:
Homotopy
Knot projections
Reidemeister moves
Spherical curves
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Summary: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.
ISSN:0166-8641
1879-3207
DOI:10.1016/j.topol.2017.04.021