FINDING KNOT INVARIANTS FROM DIAGRAM COLOURING

A traditional method of finding topological invariants of a knot in 3-dimensional euclidean space is to colour the arcs of a planar diagram and use this to extract invariants of the knot such as the fundamental group. This method can be extended in many ways to other kinds of codimension 2 embeddings. Moreover the new algebraic objects which arise quite naturally from these generalisations such as quandles, racks, biquandles etc are of interest in their own right. In this paper we shall give a brief overview of the methods and the new algebraic structures.