Tackling the Trefoils

Roger Fenn

Tackling the Trefoils

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arxiv 1110.0582 v1 pith:EQULDUPM submitted 2011-10-04 math.GT math.RA

Roger Fenn This is my paper · ORCID

classification math.GTmath.RA

keywords handedbiquandletrefoildistinguishesleftquandlerightthree-colouring

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The classical trefoil is famous for having a three-colouring which distinguishes it from the unknot. The three-colouring is also notorious for not distinguishing the right handed from the left handed trefoil. However with a bit of tweaking the three colours can also be used for this task. What lies behind the method is a new operation on biracks called doubling which converts the 3-colour quandle into a biquandle. Colouring with this biquandle distinguishes the right handed from the left handed trefoil. Equivalently it defines an element of the homology of the quandle or biquandle classifying space.

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