Reorienting quandle orbits

TL;DR

This paper examines the concept of orientation-reversal in quandle orbits, motivated by knot theory, and finds that the natural approach does not work well for medial quandles.

Contribution

It highlights a limitation of the natural orientation-reversal concept specifically in the context of medial quandles.

Findings

Natural orientation-reversal is unsuited for medial quandles.

The paper clarifies the behavior of quandle orbits under orientation-reversal.

It suggests the need for alternative approaches in medial quandle theory.

Abstract

Motivated by knot theory, it is natural to define the orientation-reversal of a quandle orbit by inverting all the translations given by elements of that orbit. In this short note we observe that this natural notion is unsuited to medial quandles.