Sir Isaac Newton

Isaac Newton Institute for Mathematical Sciences

Mathematical Gates

11. Mathematical Gates (Faulkes Gatehouse)

The medallions in these gates, created by John Robinson, depict the only two knots with at most eleven crossings having the same (trivial) Alexander polynomial as the unknot. The North gate shows the knot studied by S Kinoshita and H Terasaka, while the South gate shows the knot discovered by JH Conway in his classification of eleven-crossing knots. Related as they are by Conway mutation, this pair of knots cannot be distinguished by any skein invariant. That they are topologically distinct can be proved by investigating representations of knot groups into finite matrix groups, by determination of knot genus, or by use of certain quantum invariants.

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