A SURVEY OF QUANDLE IDEAS

By J. Scott Carter. 2010

85 citations recorded by the source corpus.

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.

Subfields: Geometry and Topology, Mathematical Physics

View Paper: https://www.semanticscholar.org/paper/9d7a68f54dfd331483e6dec4cf09949ef46c9eff

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In Geometry and Topology

In Mathematical Physics

Citations in the corpus

The structure of medial quandles (2014, background): “Affine quandles of the form Aff(A,−1) are called dihedral quandles [4], or cores of abelian groups [28].”
Connected quandles and transitive groups (2014, methodology): “dles originated with Joyce’s paper [24] and the introduction of the knot quandle, a complete invariant of oriented knots. Subsequently, quandles have been used as the basis of various knot invariants [4, 5, 6] and in algorithms on knot recognition [6, 14]. But the roots of quandle theory are much ol”