Volume 16, issue 6 (2016)

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The length of a $3$–cocycle of the $5$–dihedral quandle

Shin Satoh

Algebraic & Geometric Topology 16 (2016) 3325–3359
Abstract

We determine the length of the Mochizuki $3$–cocycle of the $5$–dihedral quandle. This induces that the $2$–twist-spun figure-eight knot and the $2$–twist-spun $\left(2,5\right)$–torus knot have the triple point number eight.

 Dedicated to Professor Taizo Kanenobu on the occasion of his 60th birthday
Keywords
surface-knot, triple point number, quandle, cocycle invariant, coloring
Primary: 57Q45
Secondary: 57Q35
Publication
Received: 1 August 2015
Revised: 5 October 2015
Accepted: 20 October 2015
Published: 15 December 2016
Authors
 Shin Satoh Department of Mathematics Kobe University Rokkodai-cho 1-1 Nada-ku Kobe 657 8501 Japan