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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 (2,5)–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
Mathematical Subject Classification 2010
Primary: 57Q45
Secondary: 57Q35
References
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