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R-equivalence of quandle colorings and inner automorphisms

  • Mai Sato
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Abstract

R-equivalence is an equivalence relation on the set of colorings of an oriented knot diagram by a quandle. In this paper, we show that a certain subgroup of the inner automorphism group of a quandle acts on the R-equivalence class of a given coloring by the quandle. We also determine the R-equivalence classes of colorings of a diagram of a $2$-bridge knot by a dihedral quandle completely, under a certain condition.

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Cite

BibTeXRIS
BibTeX
@misc{sato2026requivalence,
  title = {{R-equivalence of quandle colorings and inner automorphisms}},
  author = {Mai Sato},
  howpublished = {arXiv},
  year = {2026},
  month = sep,
  doi = {10.48550/arxiv.2608.30132},
  eprint = {2608.30132},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2608.30132},
}
RIS
TY  - UNPB
TI  - R-equivalence of quandle colorings and inner automorphisms
AU  - Mai Sato
PY  - 2026
DA  - 2026/09/29
PB  - arXiv
DO  - 10.48550/arxiv.2608.30132
UR  - https://arxiv.org/abs/2608.30132
AB  - R-equivalence is an equivalence relation on the set of colorings of an oriented knot diagram by a quandle. In this paper, we show that a certain subgroup of the inner automorphism group of a quandle acts on the R-equivalence class of a given coloring by the quandle. We also determine the R-equivalence classes of colorings of a diagram of a $2$-bridge knot by a dihedral quandle completely, under a certain condition.
ER  -