R-equivalence of quandle colorings and inner automorphisms

Mai Sato

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arXiv · 2608.30132

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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Mai Sato. 2026-08-31. R-equivalence of quandle colorings and inner automorphisms. https://arxiv.org/abs/2608.30132

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