Thirty-two equivalence relations on knot projections

Noboru Ito; Yusuke Takimura

doi:10.1016/j.topol.2017.04.021

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arXiv · 2012.02612

Thirty-two equivalence relations on knot projections

Noboru Ito·Yusuke Takimura

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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.

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Noboru Ito, Yusuke Takimura. 2020-12-04. Thirty-two equivalence relations on knot projections. https://doi.org/10.1016/j.topol.2017.04.021

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