A Survey of Quandle Ideas

TL;DR

This survey provides an overview of quandle theory, highlighting its algebraic role in knot theory and its various applications, especially focusing on quandle cocycle invariants.

Contribution

It offers a concise introduction to quandles and summarizes their diverse applications, serving as a guide for future research in the area.

Findings

Quandles encode Reidemeister moves algebraically.

Applications of quandles extend beyond knot theory.

Quandle cocycle invariants are a key area of study.

Abstract

This article surveys many aspects of the theory of quandles which algebraically encode the Reidemeister moves. In addition to knot theory, quandles have found applications in other areas which are only mentioned in passing here. The main purpose is to give a short introduction to the subject and a guide to the applications that have been found thus far for quandle cocycle invariants.