2014/10/10 by Ayumu Inoue, Inoue, Ayumu
Computer Science · Mathematics · #51M04 #57M25 #FOS: Mathematics #Geometric Topology (math.GT) #Geometric and Algebraic Topology #Homotopy and Cohomology in Algebraic Topology #Logic, programming, and type systems
paper · pdf · doi:10.48550/arxiv.1410.2666
openalex publication_date 2014/10/10 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
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 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.