R-equivalence classes of $\mathrm{Rot} \mathbb{E}^{2}$-colorings of torus knots

Mai Sato

R-equivalence classes of $\mathrm{Rot} \mathbb{E}^{2}$-colorings of torus knots

Geometric Topology 2025-01-14 v1

Authors: Mai Sato

Abstract

We introduce a new equivalence relation, named R-equivalence relation, on the set of colorings of an oriented knot diagram by a quandle. We determine the R-equivalence classes of colorings of a diagram of a torus knot by a quandle, called $\mathrm{Rot} \mathbb{E}^{2}$ , under a certain condition.

Keywords

R-equivalence torus knots quandle coloring oriented knot diagram Rot $\mathbb{E}^{2}$

Cite

@article{arxiv.2501.07031,
  title  = {R-equivalence classes of $\mathrm{Rot} \mathbb{E}^{2}$-colorings of torus knots},
  author = {Mai Sato},
  journal= {arXiv preprint arXiv:2501.07031},
  year   = {2025}
}

Comments

28 pages, 13 figures

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