On colorability of knots by rotations, Torus knot and PL trochoid

Ayumu Inoue

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arXiv · 1410.2666

On colorability of knots by rotations, Torus knot and PL trochoid

Ayumu Inoue

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Abstract

The set consisting of all rotations of the Euclidean plane is equipped with a quandle structure. We show that a knot is colorable by this quandle if and only if its Alexander polynomial has a root on the unit circle in $\mathbb{C}$. Further we enumerate all non-trivial colorings of a torus knot diagram by the quandle using PL trochoids. As an application of these results, we have the complete factorization of the Alexander polynomial of the torus knot.

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Ayumu Inoue. 2014-10-10. On colorability of knots by rotations, Torus knot and PL trochoid. https://arxiv.org/abs/1410.2666

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